Zelikin, Mikhail Il'ich

Total publications: 96 (85)
in MathSciNet: 88 (78)
in zbMATH: 74 (69)
in Web of Science: 48 (40)
in Scopus: 46 (45)
Cited articles: 57
Citations in Math-Net.Ru: 112
Citations in Web of Science: 64
Citations in Scopus: 87
Presentations: 22

Number of views:
This page:7777
Abstract pages:27692
Full texts:10208
Zelikin, Mikhail Il'ich
Corresponding member of RAS
Doctor of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 11.02.1936
Keywords: Optimal Control Theory, Chattering control, multiple integrals, cross ratio, Riccati equation, phase constraints, Pontryagin's maximum principle, Lagrangian manifolds, blow up.
UDC: 512.542, 517.551, 517.958, 517.977, 517.977.5, 519.9, 517
MSC: 37K10, 37K20


Optimal control theory, differential equations, differential games.

Main publications:
  1. M. I. Zelikin, Control Theory and Optimization I. Homogeneous Spaces and the Riccati Equation in the Calculus of Veriations, Springer-Verlag, Berlin, 2000  mathscinet
  2. M. I. Zelikin, V. F. Borisov, Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, MA, 1994  mathscinet  zmath
  3. M. I. Zelikin, Optimal control and variational calculus., URSS, Moscow, 2004
  4. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Mat. Sb., 195:6 (2004), 57–70  mathnet  mathscinet  zmath
  5. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, CMFD, 19, 2006, 45–69  mathnet
List of publications on Google Scholar

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. L. V. Lokutsievskiy, M. I. Zelikin, “The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary”, ESAIM: COCV, 26 (2020), 15 , 36 pp., arXiv: 1905.02028  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1);
2. E. F. Mishchenko, A. S. Mishchenko, M. I. Zelikin, “On the Adequacy of Mathematical Models in Control Theory, Physics and Ecology, Finished”, Math. Ed., 2020, no. 1(93), 2–14  mathnet

3. M. I. Zelikin, “Fractal Theory of Saturn's Ring. II: Electromagnetic Phenomena”, Proc. Steklov Inst. Math., 304 (2019), 153–159  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
4. M. I. Zelikin, Yu. S. Osipov, “Minimal submanifolds of spheres and cones”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 100–107  mathnet  crossref  isi  elib  scopus
5. Yu. S. Osipov, M. I. Zelikin, “Fields of smooth compact minimal surfaces”, Russ. J. Math. Phys., 26:2 (2019), 174–179  mathnet  crossref  mathscinet  zmath  isi  scopus
6. E. F. Mishchenko, A. S. Mishchenko, M. I. Zelikin, “On the Adequacy of Mathematical Models in Control Theory, Physics and Ecology”, Math. Ed., 2019, no. 4(92), 2–16  mathnet  mathscinet

7. L. V. Lokutsievskiy, M. I. Zelikin, “Hessian measures in the aerodynamic Newton problem”, J. Dyn. Control Syst., 24:3 (2018), 475–495  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
8. M. I. Zelikin, “Genius. In the Memory of I. Shafarevich”, Math. Ed., 2018, no. 1(85), 2–4  mathnet  elib

9. M. I. Zelikin, L. V. Lokoutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Math. Notes, 102:4 (2017), 521–532  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus (cited: 3)
10. M. I. Zelikin, “An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals”, Izv. Math., 81:5 (2017), 973–984  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus
11. M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Typicality of Chaotic Fractal Behavior of Integral Vortices in Hamiltonian Systems with Discontinuous Right Hand Side”, Journal of Mathematical Sciences, 221:1 (2017), 1–136  mathnet  crossref

12. M. I. Zelikin, “Fractal Theory of Saturn's Ring”, Proc. Steklov Inst. Math., 291 (2015), 87–101  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus (cited: 1)
13. S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
14. M. I. Zelikin, A. O. Ivanov, B. S. Kashin, A. S. Mishchenko, Yu. V. Nesterenko, A. A. Oshemkov, F. Yu. Popelenskii, V. A. Sadovnichii, A. A. Tuzhilin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, “Academician Anatolii Timofeevich Fomenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 6, 66–68  mathnet

15. M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 4)
16. M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Stochastic dynamics of lie algebras of Poisson brackets in neighborhoods of nonsmoothness points of Hamiltonians”, Dokl. Math., 87:3 (2013), 259–263  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 1)
17. R. Hildebrand, L. V. Lokoutsievskiy, M. I. Zelikin, “Generic fractal structure of finite parts of trajectories of piecewise smooth hamiltonian systems”, Russ. J. Math. Phys., 20:1 (2013), 25–32  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  elib  scopus (cited: 4)

18. V. F. Borisov, V. V. Gael, M. I. Zelikin, “Chattering regimes and Lagrangian manifolds in problems with phase constraints”, Izv. Math., 76:1 (2012), 1–38  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
19. M. I. Zelikin, “Theory and applications of the problem of Euler elastica”, Russian Math. Surveys, 67:2 (2012), 281–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
20. M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83  mathnet  crossref  mathscinet  zmath  isi (cited: 12)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)
21. Yu. S. Osipov, M. I. Zelikin, “Higher-order elastics and elastic hulls”, Russ. J. Math. Phys., 19:2 (2012), 234–243  mathnet  crossref  mathscinet  zmath  isi  elib  scopus (cited: 2)
22. Yu. S. Osipov, M. I. Zelikin, “Multidimensional generalizations of Jacobi's envelope theorem”, Russ. J. Math. Phys., 19:1 (2012), 101–106  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  elib  scopus (cited: 3)

23. M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 3)
24. M. I. Zelikin, “Lev Semenovich Pontryagin: reminiscences and reflections”, Istor.-Mat. Issled. (2), 2011, no. 14(49), 77–84, 357–358  mathscinet  zmath

25. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Optimal synthesis in an infinite-dimensional space”, Proc. Steklov Inst. Math., 271 (2010), 34–52  mathnet  crossref  mathscinet  isi (cited: 2)  elib  elib  scopus (cited: 2)
26. M. I. Zelikin, V. F. Borisov, “Geometry of extremals with a countable number of contact points with the boundary of the phase constraint”, Dokl. Akad. Nauk, 430:1 (2010), 7–12  mathscinet  zmath
27. Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov, “In memory of Evgenii Frolovich Mishchenko”, Proc. Steklov Inst. Math., 271 (2010), 1–2  mathnet  crossref  mathscinet  isi  elib

28. M. I. Zelikin, “Chattering control in infinite-dimensional spaces”, Tezisy dokladov, Suzdal, 2009, 186

29. M. I. Zelikin, “A criterion for the symmetry of a spectrum”, Dokl. Akad. Nauk, 418:6 (2008), 737–740  mathnet  mathscinet

30. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Extremals with accumulation of switchings in infinite-dimensional spaces”, J. Math. Sci., 160:2 (2009), 139–196  crossref  mathscinet  zmath  elib (cited: 1)  scopus (cited: 1)
31. M. I. Zelikin, L. V. Lokutsievskii, R. A. Usachev, “Vortex singularities of optimal strategies in search games”, J. Math. Sci., 160:2 (2009), 197–220  crossref  mathscinet  zmath  elib  scopus (cited: 1)

32. J. Appl. Math. Mech., 70:2 (2006), 264–273  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 2)

33. M. I. Zelikin, L. A. Manita, “Accumulation of Switchings in Distributed Parameter Problems”, Journal of Mathematical Sciences, 151:6 (2008), 3506–3542  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)
34. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, Journal of Mathematical Sciences, 151:6 (2008), 3473–3496  mathnet  crossref  zmath  elib (cited: 5)  scopus (cited: 7)

35. M. I. Zelikin, N. B. Melnikov, “The Bellman function and optimal synthesis in control problems with nonsmooth constraints”, J. Math. Sci. (N. Y.), 121:2 (2004), 2281–2294  mathnet  crossref  mathscinet  zmath
36. M. I. Zelikin, “Optimal problems on Hölder function spaces”, J. Math. Sci. (N. Y.), 121:2 (2004), 2265–2280  mathnet  crossref  mathscinet  zmath

37. M. I. Zelikin, “Geometry of operator cross ratio”, Sb. Math., 197:1 (2006), 37–51  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
38. V. I. Arnol'd, L. R. Volevich, A. A. Gonchar, S. S. Demidov, M. I. Zelikin, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, A. V. Mikhalev, S. P. Novikov, I. V. Yaschenko, “Vladimir Mikhailovich Tikhomirov (on his 70th birthday)”, Russian Math. Surveys, 61:1 (2006), 189–192  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

39. V. I. Arnol'd, A. S. Demidov, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, E. F. Mishchenko, K. Yu. Osipenko, A. B. Sossinski, M. A. Tsfasman, V. A. Uspenskii, M. N. Vyalyi, I. V. Yaschenko, M. I. Zelikin, “Vladimir M. Tikhomirov”, Mosc. Math. J., 5:1 (2005), 295  mathnet  mathscinet

40. M. I. Zelikin, “An efficient criterion for optimality in terms of two solutions of the Riccati equation”, Dokl. Akad. Nauk, 397:3 (2004), 300–303  mathnet  mathscinet  zmath  scopus
41. J. Appl. Math. Mech., 68:4 (2004), 617–622  crossref  mathscinet  zmath  isi  scopus  scopus
42. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Sb. Math., 195:6 (2004), 819–831  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 4)

43. M. I. Zelikin, V. F. Borisov, “Singular optimal regimes in problems of mathematical economics”, J. Math. Sci. (N. Y.), 130:1 (2005), 4409–4570  crossref  mathscinet  zmath  scopus (cited: 12)

44. M. I. Zelikin, “Hölderian extremal problems”, Patterns and waves (Saint Petersburg, 2002), AkademPrint, St. Petersburg, 2003, 412–432  mathscinet
45. M. I. Zelikin, “The $\zeta$-function of the cross-ratio on Sato's Grassmannian as an integral invariant of the Kadomtsev-Petviashvili hierarchy”, Dokl. Akad. Nauk, 389:2 (2003), 159–163  mathnet (cited: 1)  mathscinet  zmath
46. M. I. Zelikin, V. F. Borisov, “Optimal chattering feedback control”, J. Math. Sci. (N. Y.), 114:3 (2003), 1227–1344  mathnet  crossref  mathscinet  zmath

47. M. I. Zelikin, “Chattering on optimal trajectories of Hölder problems”, Sb. Math., 193:5 (2002), 669–683  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
48. M. I. Zelikin, “The Structure of Optimal Synthesis in the Vicinity of Singular Manifolds for Problems Affine with Respect to Control”, Proc. Steklov Inst. Math., 236 (2002), 164–185  mathnet  mathscinet  zmath

49. Differ. Equ., 37:9 (2001), 1217–1223  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
50. M. I. Zelikin, “Optimal control in Hölder classes of functions”, Dokl. Akad. Nauk, 378:6 (2001), 733–736  mathnet  mathscinet  zmath
51. M. I. Zelikin, N. B. Melnikov, R. Hildebrand, “The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems”, Proc. Steklov Inst. Math., 233 (2001), 116–142  mathnet  mathscinet  zmath
52. M. I. Zelikin, L. F. Zelikina, R. Hildebrand, “Asymptotics of Optimal Synthesis for One Class of Extremal Problems”, Proc. Steklov Inst. Math., 233 (2001), 87–115  mathnet  mathscinet  zmath
53. M. I. Zelikin, “Synthesis of Optimal Trajectories That Defines the Reeb Foliation”, Proc. Steklov Inst. Math., 233 (2001), 81–86  mathnet  mathscinet  zmath
54. A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1187–1191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi

55. V. F. Borisov, M. I. Zelikin, “Approaching the intermediate thrust modes in control problems of space navigation”, Russ. J. Math. Phys., 7:2 (2000), 127–146  mathscinet  zmath  isi  scopus
56. M. I. Zelikin, “To the theory of chattering control”, Spectral and evolution problems (Sevastopol', 1999), Vol. 10, Natl. Taurida Univ. “V. Vernadsky”, Simferopol', 2000, 170–172  mathscinet
57. M. I. Zelikin, Control theory and optimization. I, Homogeneous spaces and the Riccati equation in the calculus of variations, Encyclopaedia of Mathematical Sciences, 86, Springer-Verlag, Berlin, 2000 , xii+284 pp.  crossref  mathscinet  zmath

58. Differential Equations, 35:11 (1999), 1489–1493 (2000)  mathnet  mathscinet  zmath  isi (cited: 6)  scopus (cited: 4)
59. M. I. Zelikin, “The asymptotics of the deviation of a functional from its optimal value when chattering is replaced by a suboptimal regime”, Russian Math. Surveys, 54:3 (1999), 662–664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  scopus (cited: 2)
60. M. I. Zelikin, L. F. Zelikina, “Exact Constants in Kolmogorov-Type Inequalities”, Proc. Steklov Inst. Math., 227 (1999), 131–139  mathnet  mathscinet  zmath
61. M. I. Zelikin, “Optimal Synthesis Containing Successively Inserted Chattering Bundles”, Proc. Steklov Inst. Math., 224 (1999), 137–148  mathnet  mathscinet  zmath
62. M. I. Zelikin, V. A. Il'in, N. N. Krasovskiĭ, et al., “Lyudmila Filippovna Zelikina”, Differential Equations, 35:6 (1999), 856–857  mathnet  mathscinet  isi

63. M. I. Zelikin, “Cartan–Siegel homogeneous domains as integral manifolds of the complex Riccati-type equation”, Proc. Steklov Inst. Math., 220 (1998), 126–137  mathnet  mathscinet  zmath
64. M. I. Zelikin, “A quadratic system of partial differential equations that is associated with the problem of minimizing a multiple integral”, Dokl. Akad. Nauk, 358:1 (1998), 7–9  mathnet  mathscinet  zmath  isi  scopus
65. M. I. Zelikin, Odnorodnye prostranstva i uravnenie Rikkati v variatsionnom ischislenii, Faktorial, M., 1998 , 250 pp.  zmath
66. M. I. Zelikin, L. F. Zelikina, “The structure of optimal synthesis in a neighbourhood of singular manifolds for problems that are affine in control”, Sb. Math., 189:10 (1998), 1467–1484  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 2)
67. N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Russian Math. Surveys, 53:5 (1998), 1071–1078  mathnet  crossref  crossref  mathscinet  zmath  isi

68. M. I. Zelikin, “One-parameter families of solutions to a class of PDE optimal control problems”, Optimization methods in partial differential equations (South Hadley, MA, 1996), Contemp. Math., 209, Amer. Math. Soc., Providence, RI, 1997, 339–349  crossref  mathscinet  zmath
69. M. I. Zelikin, “On the connection generated by the problem of minimizing a multiple integral”, Sb. Math., 188:1 (1997), 61–74  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus

70. M. I. Zelikin, “The Fuller phenomenon in problems of vibration of two linked oscillators”, Dynamical systems, 1, J. Math. Sci., 78:5 (1996), 626–631  crossref  mathscinet  zmath  scopus (cited: 3)
71. M. I. Zelikin, “Optimum control of solid body rotation”, Dokl. Akad. Nauk, 346:3 (1996), 334–336  mathnet  zmath

72. M. I. Zelikin, “Totally extremal manifolds for optimal control problems”, Semigroups in algebra, geometry and analysis (Oberwolfach, 1993), de Gruyter Exp. Math., 20, de Gruyter, Berlin, 1995, 339–354  mathscinet  zmath
73. M. I. Zelikin, “Irregularity of optimal control in regular extremal problems”, Fundam. Prikl. Mat., 1:2 (1995), 399–408  mathnet  mathscinet  zmath

74. M. I. Zelikin, V. F. Borisov, Theory of chattering control, With applications to astronautics, robotics, economics, and engineering, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 1994 , xvi+242 pp.  mathscinet  zmath
75. M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 213–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  scopus (cited: 1)

76. M. I. Zelikin, V. F. Borisov, “Regimes with frequented switches in the problems of optimal control”, Proc. Steklov Inst. Math., 197 (1993), 95–186  mathnet  mathscinet  zmath

77. M. I. Zelikin, V. F. Borosov, “Optimal synthesis containing chattering arcs and singular arcs of the second order”, Nonlinear synthesis (Sopron, 1989), Progr. Systems Control Theory, 9, Birkhäuser Boston, Boston, MA, 1991, 283–296  mathscinet

78. M. I. Zelikin, “On the theory of the matrix Riccati equation”, Math. USSR-Sb., 73:2 (1992), 341–354  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  scopus (cited: 2)

79. M. I. Zelikin, V. F. Borisov, “Synthesis in problems of optimal control containing trajectories with participating switchings and singular trajectories of the second order”, Math. Notes, 47:1 (1990), 41–49  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 1)

80. Soviet Math. Dokl., 39:1 (1989), 188–191  mathnet  mathscinet  zmath  isi

81. J. Appl. Math. Mech., 52:6 (1988), 731–737 (1990)  crossref  mathscinet  zmath  isi  scopus (cited: 1)
82. M. I. Zelikin, “Group symmetry in degenerate extremal problems”, Russian Math. Surveys, 43:2 (1988), 189–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus
83. M. I. Zelikin, “Synthesis of optimal trajectories on representation spaces of Lie groups”, Math. USSR-Sb., 60:2 (1988), 533–546  mathnet  crossref  mathscinet  zmath  scopus

84. M. I. Zelikin, “The search for singular extremals”, Stochastic optimization (Kiev, 1984), Lecture Notes in Control and Inform. Sci., 81, Springer, Berlin, 1986, 738–746  crossref  mathscinet
85. A. G. Vitushkin, M. I. Zelikin, N. N. Krasovskii, S. P. Novikov, Yu. S. Osipov, K. A. Sitnikov, “Nicolai Terent'evich Tynyanskii (obituary)”, Russian Math. Surveys, 41:4 (1986), 173–174  mathnet  crossref  mathscinet  adsnasa  isi

86. M. I. Zelikin, Optimalnoe upravlenie i variatsionnoe ischislenie, Izd-vo MGU, M., 1985 , 96 pp.  mathscinet  zmath
87. M. I. Zelikin, “Minimization of integrals of differential forms, and degenerate variational problems”, Wiss. Z. Tech. Hochsch. Leuna-Merseburg, 27:5 (1985), 526–534  mathscinet  zmath
88. M. I. Zelikin, “On the singular arcs”, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 14:2 (1985), 75–88, R1–R15  mathscinet  zmath  scopus (cited: 5)

89. M. I. Zelikin, “Necessary conditions for optimality of singular trajectories in problems that are linear with respect to control”, Some problems in modern analysis, Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1984, 35–41  mathscinet  zmath
90. M. I. Zelikin, “Minimization of integrals of differential forms”, Dokl. Akad. Nauk SSSR, 278:5 (1984), 1057–1059  mathnet  mathscinet  zmath  isi (cited: 1)
91. M. I. Zelikin, “On the theory of linear control problems”, Dokl. Akad. Nauk SSSR, 277:4 (1984), 782–785  mathnet (cited: 1)  mathscinet  zmath  isi (cited: 3)

92. M. I. Zelikin, “Optimality conditions for singular trajectories in a problem of curvilinear integral minimization”, Dokl. Akad. Nauk SSSR, 267:3 (1982), 528–531  mathnet  mathscinet  mathscinet  zmath  isi (cited: 2)

93. D. V. Anosov, V. I. Arnol'd, M. I. Zelikin, A. N. Kolmogorov, O. V. Lokutsievskii, Yu. S. Osipov, Ya. G. Sinai, V. M. Tikhomirov, M. V. Jakobson, “Vladimir Mikhailovich Alekseev (obituary)”, Russian Math. Surveys, 36:4 (1981), 201–206  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus

94. M. I. Zelikin, B. Yu. Sternin, “A system of integral equations that arises in the problem of S. L. Sobolev”, Siberian Math. J., 18:1 (1977), 72–76  mathnet  crossref  mathscinet  mathscinet  zmath  isi

95. M. I. Zelikin, “A certain differential game with incomplete information”, Dokl. Akad. Nauk SSSR, 202 (1972), 998–1000  mathnet (cited: 2)  mathscinet  mathscinet  zmath

96. M. I. Zelikin, N. T. Tynyanskii, “Determined differential games”, Uspekhi Mat. Nauk, 20:4(124) (1965), 151–157  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Задача Ньютона о телах минимального сопротивления при отказе от предположения о вращательной симметрии
M. I. Zelikin, L. V. Lokutsievskiy
Meetings of the Moscow Mathematical Society
May 5, 2020 18:30
2. Задача Ньютона о телах минимального сопротивления при отказе от предположения о вращательной симметрии
M. I. Zelikin, L. V. Lokutsievskiy
Differential geometry and applications
March 16, 2020 16:45
3. Задача Ньютона о телах минимального сопротивления при отказе от предположения о вращательной симметрии.
M. I. Zelikin, L. V. Lokutsievskiy
Dobrushin Mathematics Laboratory Seminar
January 14, 2020 16:00
4. Точное аналитическое решение задачи Ньютона о телах минимального сопротивления при отказе от предположения о вращательной симметрии
M. I. Zelikin
Mathematical Workshop of the School of Applied Mathematics and Computer Science (MIPT)
November 29, 2019 18:30   
5. Об аэродинамической задаче Ньютона без предположения об осевой симметрии
M. I. Zelikin, L. V. Lokutsievskiy
Differential equations, analysis and control: theory and applications
November 25, 2019 18:30
6. Аналитическое решение аэродинамической задачи Ньютона без предположения об осевой симметрии
M. I. Zelikin, L. V. Lokutsievskiy
Problems of Mathematical Control Theory
May 21, 2019 11:00
7. Solutions of Newton's aerodynamic problem without axial symmetry
M. I. Zelikin, L. V. Lokutsievskiy
International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin
December 14, 2018 12:15   
8. Поля гладких компактных минимальных многообразий
M. I. Zelikin
Geometric Theory of Optimal Control
December 5, 2018 18:30
9. Singular extremals in the generalised Fuller problem
M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskiy
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 1, 2017 15:45   
10. Analogue of Pontryagin's maximum principle for multiple integrals minimization problems
M. I. Zelikin
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 1, 2017 12:35   
11. An analogue of the Pontryagin maximum principle for multiple integral minimizing problems
M. I. Zelikin
International conference "Dynamical Systems: Inverse Problems, Stability and Control Processes" dedicated to the 80th birthday of Yu. S. Osipov
September 22, 2016 11:00   
12. Заседание посвящено памяти Дмитрия Викторовича Аносова
A. M. Stepin, L. M. Lerman, V. Z. Grines, S. Yu. Pilyugin, M. I. Zelikin, V. P. Leksin, A. V. Klimenko, Yu. S. Ilyashenko
Meetings of the Moscow Mathematical Society
April 7, 2015
13. Фрактальная структура оптимального синтеза
M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand
All-Moscow regular scientific seminar "Control Theory and Optimization"
December 2, 2014 11:30
14. Chaos in optimal synthesis in problems with multidimensional control (part I)
M. I. Zelikin
The International Conference "Geometric Control Theory and Analysis on Metric Structures"
August 4, 2014 15:00
15. Singular orbits in hamiltonian systems with discontinous right term
M. I. Zelikin, L. V. Lokutsievskii
Differential geometry and applications
March 24, 2014 16:45
16. Chaotic dynamics of optimal trajectories in problems with multidimensional control
M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 11:10   
17. Stochastic dynamics of Lie algebras of Poisson brackets in a neighbourhood of the points where the Hamiltonian is not smooth
M. I. Zelikin
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
April 3, 2013 16:45
18. Стохастическая динамика алгебр Ли скобок Пуассона в окрестности точек негладкости гамильтониана
M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand
Meetings of the Moscow Mathematical Society
February 12, 2013 18:30
19. Euler's elastics and elastic shells
M. I. Zelikin
Differential geometry and applications
November 26, 2012 16:45
20. Fields of extremals for multiple integrals
M. I. Zelikin
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 23, 2011 16:45
21. Теория поля экстремалей для функционалов типа кратных интегралов
M. I. Zelikin
Meetings of the Moscow Mathematical Society
March 23, 2010
22. Фазовый портрет с накоплением переключений в бесконечномерном пространстве
M. I. Zelikin
Seminar "Optimal Control and Dynamical Systems"
April 2, 2008 12:00

Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021