Bolotin S., “Second species periodic orbits of the elliptic 3 body problem”, Celestial Mech. Dynam. Astronom., 93:1-4 (2006), 343–371
Bolotin S., “Symbolic dynamics of almost collision orbits and skew products of symplectic maps”, Nonlinearity, 19:9 (2006), 2041–2063
Bolotin S., Negrini P., Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system, In preparation
Bolotin S. V., MacKay R. S., “Periodic and chaotic trajectories of the second species for the $n$-centre problem”, Celestial Mech. Dynam. Astronom., 77:1 (2000), 49–75
Bolotin S. V., Treschev D. V., “Hill's formula”, Uspekhi Mat. Nauk, 65:2 (2010), 3–70; English transl.: Russian Math. Surveys, 65:2 (2010), 191–257
S. V. Bolotin, Uspekhi Mat. Nauk, 73 (2018) (to appear)
2017
2.
Sergey V. Bolotin, “Degenerate Billiards in Celestial Mechanics”, Regul. Chaotic Dyn., 22:1 (2017), 27–53
3.
S. V. Bolotin, V. V. Kozlov, “Topological approach to the generalized $n$-centre problem”, Russian Math. Surveys, 72:3 (2017), 451–478 (cited: 1)
4.
S. V. Bolotin, V. V. Kozlov, “Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom”, Izv. Math., 81:4 (2017), 671–687 (cited: 2) (cited: 1)
2016
5.
S. V. Bolotin, “Degenerate billiards”, Proc. Steklov Inst. Math., 295 (2016), 45–62 (cited: 3) (cited: 3)
2015
6.
S. V. Bolotin, V. V. Kozlov, “Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problem”, Izv. Math., 79:5 (2015), 894–901 (cited: 1) (cited: 2)
7.
S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030 (cited: 10) (cited: 7)
2014
8.
S. Bolotin, P. H. Rabinowitz, “Hybrid mountain pass homoclinic solutions of a class of semilinear elliptic PDEs”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 103–128 (cited: 5) (cited: 4) (cited: 4)
2013
9.
S. Bolotin, P. Negrini, “Variational approach to second species periodic solutions of Poincaré three-body problem”, Discrete Contin. Dyn. Syst., 33:3 (2013), 1009–1032 , arXiv: 1104.2288 (cited: 3) (cited: 6) (cited: 3) (cited: 6)
10.
S. V. Bolotin, T. V. Popova, “On the motion of a mechanical system inside a rolling ball”, Regul. Chaotic Dyn., 18:1-2 (2013), 159–165 (cited: 8) (cited: 7) (cited: 7) (cited: 9) (cited: 7)
11.
S. Bolotin, P. Negrini, “Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system”, Regul. Chaotic Dyn., 18:6 (2013), 774–800 (cited: 3) (cited: 1) (cited: 3) (cited: 1) (cited: 3)
12.
Sergey V. Bolotin, Tatiana V. Popova, “On the motion of a mechanical system inside a rolling ball”, Nelin. Dinam., 9:1 (2013), 51–58
2012
13.
S. V. Bolotin, “Zadacha optimalnogo upravleniya kacheniem shara s rotorami”, Nelineinaya dinam., 8:4 (2012), 837–852 (cited: 1)
14.
S. V. Bolotin, “The problem of optimal control of a Chaplygin ball by internal rotors”, Regul. Chaotic Dyn., 17:6 (2012), 559–570 (cited: 4) (cited: 3) (cited: 5) (cited: 4) (cited: 5)
2011
15.
S. Bolotin, P. H. Rabinowitz, “A note on hybrid heteroclinic solutions for a class of semilinear elliptic PDEs”, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 22:2 (2011), 151–160 (cited: 1) (cited: 1)
2010
16.
S. V. Bolotin, D. V. Treschev, “Hill's formula”, Russian Math. Surveys, 65:2 (2010), 191–257 (cited: 8) (cited: 5) (cited: 5) (cited: 7)
17.
S. V. Bolotin, A. A. Gonchar, S. P. Konovalov, E. F. Mishchenko, Yu. S. Osipov, V. A. Sadovnichii, A. G. Sergeev, Ya. V. Tatarinov, D. V. Treschev, L. D. Faddeev, “Valerii Vasil'evich Kozlov has turned 60 years old”, Russian Math. Surveys, 65:2 (2010), 389–395
18.
S. V. Bolotin, A. V. Borisov, A. A. Kilin, I. S. Mamaev, D. V. Treschev, “Valery Vasilievich Kozlov on his 60th birthday”, Regul. Chaotic Dyn., 15:4-5 (2010), 419–424
19.
A. V. Borisov, S. V. Bolotin, A. A. Kilin, I. S. Mamaev, D. V. Treschev, “Valery V. Kozlov: On the sixtieth birthday”, Nelin. Dinam., 6:3 (2010), 461–488
20.
S. V. Bolotin, A. V. Karapetyan, E. I. Kugushev, D. V. Treschev, Teoreticheskaya mekhanika, Izd-vo «Akademiya», Moskva, 2010 , 432 pp.
2007
21.
S. Bolotin, P. H. Rabinowitz, “On the multiplicity of periodic solutions of mountain pass type for a class of semilinear PDE's”, J. Fixed Point Theory Appl., 2:2 (2007), 313–331 (cited: 5) (cited: 4) (cited: 5) (cited: 5)
2006
22.
S. Bolotin, “Symbolic dynamics of almost collision orbits and skew products of symplectic maps”, Nonlinearity, 19:9 (2006), 2041–2063 (cited: 7) (cited: 9) (cited: 5) (cited: 9)
23.
S. Bolotin, R. S. MacKay, “Nonplanar second species periodic and chaotic trajectories for the circular restricted three-body problem”, Celestial Mech. Dynam. Astronom., 94:4 (2006), 433–449 (cited: 4) (cited: 10) (cited: 9) (cited: 11)
24.
S. Bolotin, P. H. Rabinowitz, “A note on heteroclinic solutions of mountain pass type for a class of nonlinear elliptic PDE's”, Contributions to nonlinear analysis, Progr. Nonlinear Differential Equations Appl., 66, Birkhäuser, Basel, 2006, 105–114 (cited: 6)
25.
S. Bolotin, “Shadowing chains of collision orbits”, Discrete Contin. Dyn. Syst., 14:2 (2006), 235–260 (cited: 6) (cited: 7) (cited: 12)
2005
26.
S. Bolotin, “Shadowing chains of collision orbits for the elliptic 3-body problem”, SPT 2004 – Symmetry and perturbation theory, World Sci. Publ., Hackensack, NJ, 2005, 51–58 (cited: 1)
27.
S. Bolotin, “Second species periodic orbits of the elliptic 3 body problem”, Celestial Mech. Dynam. Astronom., 93:1-4 (2005), 343–371 (cited: 5) (cited: 6) (cited: 5) (cited: 9)
2004
28.
S. Bolotin, A. Delshams, R. Ramírez-Ros, “Persistence of homoclinic orbits for billiards and twist maps”, Nonlinearity, 17:4 (2004), 1153–1177 (cited: 6) (cited: 6) (cited: 5) (cited: 6)
2003
29.
M. L. Bertotti, S. V. Bolotin, “Chaotic trajectories for natural systems on a torus”, Discrete Contin. Dyn. Syst., 9:5 (2003), 1343–1357 (cited: 2) (cited: 1) (cited: 2)
30.
S. V. Bolotin, P. Negrini, “Chaotic behavior in the 3-center problem”, J. Differential Equations, 190:2 (2003), 539–558 (cited: 4) (cited: 8) (cited: 8)
31.
S. V. Bolotin, R. S. MacKay, “Isochronous oscillations”, Localization and energy transfer in nonlinear systems, eds. L. Vazquez, R. S. MacKay, M.-P. Zorzano, World Sci., 2003, 217–224
2002
32.
S. Bolotin, A. Delshams, Yu. Fedorov, R. Ramírez-Ros, “Bi-asymptotic billiard orbits inside perturbed ellipsoids”, Progress in nonlinear science (Nizhny Novgorod, 2001), v. 1, RAS, Inst. Appl. Phys., Nizhniĭ Novgorod, 2002, 48–62 (cited: 1)
33.
S. V. Bolotin, P. H. Rabinowitz, “Some geometrical conditions for the existence of chaotic geodesics on a torus”, Ergodic Theory Dynam. Systems, 22:5 (2002), 1407–1428 (cited: 3) (cited: 3) (cited: 2) (cited: 4)
34.
S. Bolotin, P. Negrini, “Global regularization for the $n$-center problem on a manifold”, Discrete Contin. Dyn. Syst., 8:4 (2002), 873–892 (cited: 5) (cited: 2) (cited: 7)
2001
35.
S. V. Bolotin, “Symbolic dynamics near minimal hyperbolic invariant tori of Lagrangian systems”, Nonlinearity, 14:5 (2001), 1123–1140 (cited: 5) (cited: 7) (cited: 7) (cited: 7)
36.
S. V. Bolotin, P. Negrini, “Regularization and topological entropy for the spatial $n$-center problem”, Ergodic Theory Dynam. Systems, 21:2 (2001), 383–399 (cited: 8) (cited: 12)
2000
37.
M. L. Bertotti, S. V. Bolotin, “Kinetic energy and Lyapunov stability of equilibria of natural Lagrangian systems”, International Conference on Differential Equations (Berlin, 1999), v. 1, 2, World Sci. Publ., River Edge, NJ, 2000, 1155–1157
38.
S. V. Bolotin, R. S. Mackay, “Periodic and chaotic trajectories of the second species for the $n$-centre problem”, Celestial Mech. Dynam. Astronom., 77:1 (2000), 49–75 (cited: 12) (cited: 25) (cited: 20) (cited: 25)
39.
S. V. Bolotin, D. V. Treschev, “Remarks on the definition of hyperbolic tori of Hamiltonian systems”, Regul. Chaotic Dyn., 5:4 (2000), 401–412 (cited: 18) (cited: 27) (cited: 27)
40.
S. V. Bolotin, “Infinite number of homoclinic orbits to hyperbolic invariant tori of Hamiltonian systems”, Regul. Chaotic Dyn., 5:2 (2000), 139–156 (cited: 8) (cited: 9) (cited: 10)
41.
M. L. Bertotti, S. V. Bolotin, “On the influence of the kinetic energy on the stability of equilibria of natural Lagrangian systems”, Arch. Ration. Mech. Anal., 152:1 (2000), 65–79 (cited: 2) (cited: 1) (cited: 3) (cited: 3)
1999
42.
S. V. Bolotin, “Heteroclinic chains of skew product Hamiltonian systems”, Hamiltonian systems with three or more degrees of freedom (S'Agaró, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533, Kluwer Acad. Publ., Dordrecht, 1999, 13–25 (cited: 1) (cited: 11)
43.
S. V. Bolotin, P. H. Rabinowitz, “Minimal heteroclinic geodesics for the $n$-torus”, Calc. Var. Partial Differential Equations, 9:2 (1999), 125–139 (cited: 3) (cited: 3) (cited: 3)
44.
S. Bolotin, D. Treschev, “Unbounded growth of energy in nonautonomous Hamiltonian systems”, Nonlinearity, 12:2 (1999), 365–388 (cited: 33) (cited: 47) (cited: 30) (cited: 43)
1998
45.
M. L. Bertotti, S. V. Bolotin, “Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields”, Ann. Mat. Pura Appl. (4), 174 (1998), 253–275 (cited: 4) (cited: 5) (cited: 6)
46.
S. V. Bolotin, P. H. Rabinowitz, “Heteroclinic geodesics for a class of manifolds with symmetry”, Regul. Chaotic Dyn., 3:4 (1998), 49–62 (cited: 4) (cited: 4) (cited: 4)
47.
S. V. Bolotin, “Connecting orbits of Hamiltonian systems”, Nonlinear functional analysis and applications to differential equations (Trieste, 1997), World Sci. Publ., River Edge, NJ, 1998, 36–59
48.
S. V. Bolotin, P. H. Rabinowitz, “A variational construction of chaotic trajectories for a Hamiltonian system on a torus”, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 1:3 (1998), 541–570 (cited: 12)
49.
M. L. Bertotti, S. V. Bolotin, “Homoclinic solutions of almost periodic Hamiltonian systems”, International Conference on Differential Equations (Lisboa, 1995), World Sci. Publ., River Edge, NJ, 1998, 272–276
50.
S. V. Bolotin, P. H. Rabinowitz, “A variational construction of chaotic trajectories for a reversible Hamiltonian system”, J. Differential Equations, 148:2 (1998), 364–387 (cited: 19) (cited: 21) (cited: 17) (cited: 24)
1997
51.
S. Bolotin, P. Negrini, “A variational criterion for nonintegrability”, Russian J. Math. Phys., 5:4 (1997), 415–436 (cited: 10) (cited: 6) (cited: 13) (cited: 15)
52.
M. L. Bertotti, S. V. Bolotin, “Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff”, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 8:2 (1997), 93–100 (cited: 1)
53.
S. Bolotin, R. MacKay, “Multibump orbits near the anti-integrable limit for Lagrangian systems”, Nonlinearity, 10:5 (1997), 1015–1029 (cited: 17) (cited: 25) (cited: 23) (cited: 24)
54.
S. Bolotin, “Homoclinic trajectories of invariant sets of Hamiltonian systems”, NoDEA Nonlinear Differential Equations Appl., 4:3 (1997), 359–389 (cited: 7)
1995
55.
S. V. Bolotin, “On supports of minimal invariant measures of Hamiltonian systems”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1995, no. 6, 38–45
56.
S. Bolotin, “Homoclinic trajectories of time dependent Hamiltonian systems”, Variational and local methods in the study of Hamiltonian systems (Trieste, 1994), World Sci. Publ., River Edge, NJ, 1995, 1–16 (cited: 1)
57.
S. V. Bolotin, “Invariant sets of Hamiltonian systems and variational methods”, Proceedings of the International Congress of Mathematicians (Zürich, 1994), v. 1, 2, Birkhäuser, Basel, 1995, 1169–1178 (cited: 1)
58.
S. V. Bolotin, V. V. Kozlov, “Symmetry fields of geodesic flows”, Russian J. Math. Phys., 3:3 (1995), 279–295 (cited: 2)
59.
S. Bolotin, P. Negrini, “Asymptotic solutions of Lagrangian systems with gyroscopic forces”, NoDEA Nonlinear Differential Equations Appl., 2:4 (1995), 417–444 (cited: 2) (cited: 5)
60.
M. L. Bertotti, S. V. Bolotin, “A variational approach for homoclinics in almost periodic Hamiltonian systems”, Comm. Appl. Nonlinear Anal., 2:4 (1995), 43–57 (cited: 4)
61.
S. V. Bolotin, “Homoclinic orbits in invariant tori of Hamiltonian systems”, Dynamical systems in classical mechanics, Amer. Math. Soc. Transl. Ser. 2, 168, Amer. Math. Soc., Providence, RI, 1995, 21–90 (cited: 34)
62.
M. L. Bertotti, S. V. Bolotin, “Homoclinic solutions of quasiperiodic Lagrangian systems”, Differential Integral Equations, 8:7 (1995), 1733–1760 (cited: 2)
1994
63.
S. Bolotin, “Variational criteria for nonintegrability and chaos in Hamiltonian systems”, Hamiltonian mechanics (Toruń, 1993), NATO Adv. Sci. Inst. Ser. B Phys., 331, Plenum, New York, 1994, 173–179 (cited: 9)
1993
64.
S. V. Bolotin, P. Negrini, “Asimptoticheskie traektorii giroskopicheskikh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1993, no. 6, 66–75 (cited: 1)
65.
S. V. Bolotin, “Homoclinic orbits of geodesic flows on surfaces”, Russian J. Math. Phys., 1:3 (1993), 275–288 (cited: 4)
1992
66.
S. V. Bolotin, “Dvoyakoasimptoticheskie traektorii minimalnykh geodezicheskikh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1992, no. 1, 92–96
67.
S. V. Bolotin, “Homoclinic trajectories to minimal tori of Lagrangian systems”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1992, no. 6, 34–41 (cited: 1)
68.
S. V. Bolotin, “Variational methods for constructing chaotic motions in the dynamics of a rigid body”, J. Appl. Math. Mech., 56:2 (1992), 198–205 (cited: 2) (cited: 3)
69.
S. V. Bolotin, “Integrable billiards on surfaces of constant curvature”, Math. Notes, 51:2 (1992), 117–123 (cited: 10) (cited: 2) (cited: 8)
70.
S. V. Bolotin, “Letter to the editors: “Variational methods for constructing chaotic motions in the dynamics of a rigid body””, J. Appl. Math. Mech., 56:6 (1992), 959
1990
71.
S. V. Bolotin, “Motions that are doubly asymptotic to invariant tori in the theory of the perturbations of Hamiltonian systems”, J. Appl. Math. Mech., 54:3 (1990), 412–417 (cited: 1) (cited: 1)
72.
S. V. Bolotin, “Integriruemye bilyardy Birkgofa”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1990, no. 2, 33–36 (cited: 7)
73.
S. V. Bolotin, “Dvoyakoasimptoticheskie traektorii i usloviya integriruemo sti gamiltonovykh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1990, no. 1, 55–63 (cited: 3)
1988
74.
S. V. Bolotin, “O pervykh integralakh sistem s uprugimi otrazheniyami”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1988, no. 6, 42–45 (cited: 3)
S. V. Bolotin, “Periodic solutions of systems with gyroscopic forces”, J. Appl. Math. Mech., 51:4 (1987), 535–537 (cited: 2)
1986
77.
S. V. Bolotin, “The splitting of asymptotic surfaces”, Geometriya, differentsialnye uravneniya i mekhanika (Moskva, 1985), Izd-vo MGU, M., 1986, 52–53
78.
S. V. Bolotin, “Zamechanie o metode Rausa i gipoteze Gertsa”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1986, no. 5, 51–53 (cited: 2)
79.
S. V. Bolotin, “Uslovie neintegriruemosti po Liuvillyu gamiltonovykh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1986, no. 3, 58–64
1984
80.
S. V. Bolotin, “The effect of singularities of the potential energy on the integrability of mechanical systems”, J. Appl. Math. Mech., 48:3 (1984), 255–260 (cited: 2) (cited: 6)
81.
S. V. Bolotin, “O pervykh integralakh sistem s giroskopicheskimi silami”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1984, no. 6, 75–82 (cited: 7)
82.
S. V. Bolotin, “Neintegriruemost zadachi $n$ tsentrov pri $n>2$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1984, no. 3, 65–68 (cited: 16)
1983
83.
S. V. Bolotin, “Suschestvovanie gomoklinicheskikh dvizhenii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1983, no. 6, 98–103 (cited: 20)
1980
84.
V. V. Kozlov, S. V. Bolotin, “Ob asimptoticheskikh resheniyakh uravnenii dinamiki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1980, no. 4, 84–89 (cited: 10)
1978
85.
S. V. Bolotin, V. V. Kozlov, “Libration in systems with many degrees of freedom”, J. Appl. Math. Mech., 42:2 (1978), 256–261 (cited: 12) (cited: 25)
86.
S. V. Bolotin, “Libratsionnye dvizheniya naturalnykh dinamicheskikh si stem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1978, no. 6, 72–77 (cited: 38)
2018
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