Lerman, Lev Mikhailovich

Statistics Math-Net.Ru
Total publications: 31
Scientific articles: 24
Presentations: 7

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This page:1731
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Full texts:1759
Lerman, Lev Mikhailovich
Doctor of physico-mathematical sciences (1999)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Keywords: Hamiltonian, homoclinic, symplectic, nonautonomous, bifurcation.


Dynamical Systems.

Main publications:
  1. L. M. Lerman, L. P. Shilnikov, “O klassifikatsii grubykh neavtonomnykh sistem vtorogo poryadka s konechnym chislom yacheek”, DAN SSSR, 209:3 (1973), 544–547  mathscinet  zmath
  2. L. M. Lerman, L. P. Shilnikov, “Gomoklinicheskie struktury v beskonechnomernykh sistemakh”, Sib. matem. zhurn., 29:3 (1988), 408–417  mathscinet  zmath
  3. G. L. Alfimov, V. M. Eleonsky, N. E. Kulagin, L. M. Lerman, V. P. Silin, “On existence of nontrivial solutions for the equation $\Delta u-u+u^3=0$”, Physica D, 44 (1990), 168–177  crossref  mathscinet  zmath  adsnasa
  4. L. M. Lerman, L. P. Shil'nikov, “Homoclinical Structures in Nonautonomous Systems: Nonautonomous Chaos”, Chaos: Interdisc. J. Nonlinear Sci., 2:3, 447–454  crossref  mathscinet  zmath
  5. L. Yu. Glebsky, L. M. Lerman, “On small stationary localized solutions for the generalized 1-D Swift–Hohenberg equation”, Chaos: Interdisc. J. Nonlin. Sci., 5:2 (1995), 424–431  crossref  mathscinet  zmath
  6. L. Yu. Glebsky, L. M. Lerman, “Instability of small stationary localized solutions to a class of reversible 1+1 PDEs”, Nonlinearity, 10:2 (1997), 389–407  crossref  mathscinet  zmath  adsnasa
  7. L. M. Lerman, “Homo- and heteroclinic orbits, hyperbolic subsets in a one-parameter unfolding of a Hamiltonian system with two saddle-foci”, Regular and Chaotic Dynamics, 2:3–4 (1997), 139–155  mathscinet  zmath
  8. L. M. Lerman, Ya. L. Umanskiy, Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects), Translations of Mathematical Monographs, 176, AMS, Providence, RI, 1998  mathscinet  zmath
  9. V. Gelfreich, L. M. Lerman, “Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system”, Nonlinearity, 15 (2002), 447–457  crossref  mathscinet  zmath  adsnasa
  10. V. Gelfreich, L. M. Lerman, “Long-periodic orbits and invariant tori in a singularly perturbed Hamiltonian system”, Physica D, 176:3–4 (2003), 125–146  crossref  mathscinet  zmath  adsnasa
  11. L. M. Lerman, O. Koltsova, A. Delshams, P. Gutierrez, “Homoclinic orbits to invariant tori near a homoclinic orbit to center-center-saddle equilibrium”, Physica D: Nonlinear Phenomena, 201 (2005), 268–290  crossref  mathscinet  zmath  adsnasa
  12. L. M. Lerman, “Remarks on skew products over irrational rotations”, International Journal of Bifurcation and Chaos, 15 (2005), 3675–3689  crossref  mathscinet  zmath
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. L. M. Lerman, K. N. Trifonov, “The Topology of Symplectic Partially Hyperbolic Automorphisms of the 4-Torus”, Mat. Zametki, 108:3 (2020),  474–476  mathnet  mathscinet  elib; Math. Notes, 108:3 (2020), 462–464  isi  scopus
2. E. G. Galkina, C. E. Zaspel, B. A. Ivanov, N. E. Kulagin, L. M. Lerman, “Limiting velocity and dispersion law of domain walls in ferrimagnets close to the spin compensation point”, Pis'ma v Zh. Èksper. Teoret. Fiz., 110:7 (2019),  474–479  mathnet  elib; JETP Letters, 110:7 (2019), 481–486  isi  scopus
3. L. Lerman, A. Markova, “On symplectic dynamics near a homoclinic orbit to $1$-elliptic fixed point”, Tr. Mosk. Mat. Obs., 76:2 (2015),  309–342  mathnet  elib; Trans. Moscow Math. Soc., 76:2 (2015), 271–299  scopus
4. Vassili Gelfreich, Lev Lerman, “Separatrix Splitting at a Hamiltonian $0^2 i\omega$ Bifurcation”, Regul. Chaotic Dyn., 19:6 (2014),  635–655  mathnet  mathscinet  zmath  isi
5. Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov”, Regul. Chaotic Dyn., 19:4 (2014),  435–460  mathnet  mathscinet  zmath  isi
6. N. E. Kulagin, L. M. Lerman, “Localized solutions of a piecewise linear model of the stationary Swift–Hohenberg equation on the line and on the plane”, CMFD, 47 (2013),  60–77  mathnet; Journal of Mathematical Sciences, 202:5 (2014), 684–702  scopus
7. L. M. Lerman, D. V. Turaev, “On symmetry breaking bifurcations in reversible systems”, Nelin. Dinam., 8:2 (2012),  323–343  mathnet
8. Lev M. Lerman, Dimitry Turaev, “Breakdown of Symmetry in Reversible Systems”, Regul. Chaotic Dyn., 17:3-4 (2012),  318–336  mathnet  mathscinet  zmath  scopus
9. L. M. Lerman, N. A. Slinyakova, “On the dynamics of the piecewise-linear model of the Swift–Hohenberg equation”, Nelin. Dinam., 5:4 (2009),  569–583  mathnet
10. N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “On Radial Solutions of the Swift–Hohenberg Equation”, Trudy Mat. Inst. Steklova, 261 (2008),  188–209  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 261 (2008), 183–203  isi  elib  scopus
11. N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “Fronts, traveling fronts, and their stability in the generalized Swift–Hohenberg equation”, Zh. Vychisl. Mat. Mat. Fiz., 48:4 (2008),  693–712  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 48:4 (2008), 659–676  isi  scopus
12. L. M. Lerman, “Partial normal form near a saddle of a Hamiltonian system”, Regul. Chaotic Dyn., 11:2 (2006),  291–297  mathnet  mathscinet  zmath
13. L. M. Lerman, “Homo- and heteroclinic orbits, hyperbolic subsets in a one-parameter unfolding of a Hamiltonian system with heteroclinic contour with two saddle-foci”, Regul. Chaotic Dyn., 2:3-4 (1997),  139–155  mathnet  mathscinet  zmath
14. L. M. Lerman, Ya. L. Umanskii, “Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III. Realization”, Mat. Sb., 186:10 (1995),  89–102  mathnet  mathscinet  zmath; Sb. Math., 186:10 (1995), 1477–1491  isi
15. L. M. Lerman, Ya. L. Umanskii, “Isoenergetic classification of integrable Hamiltonian systems in a neighborhood of a simple elliptic point”, Mat. Zametki, 55:5 (1994),  88–97  mathnet  mathscinet  zmath; Math. Notes, 55:5 (1994), 496–501  isi
16. L. M. Lerman, Ya. L. Umanskii, “Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb{R}^2$ in extended neighborhoods of simple singular points. II”, Mat. Sb., 184:4 (1993),  105–138  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 78:2 (1994), 479–506  isi
17. L. M. Lerman, Ya. L. Umanskii, “Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb{R}^2$ in extended neighborhoods of simple singular points. I”, Mat. Sb., 183:12 (1992),  141–176  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 77:2 (1994), 511–542  isi
18. G. L. Alfimov, V. M. Eleonskii, N. E. Kulagin, L. M. Lerman, V. P. Silin, “Three-dimensional optical structures described by the nonlinear Helmholtz equation”, Kvantovaya Elektronika, 17:7 (1990),  943–944  mathnet [Sov J Quantum Electron, 20:7 (1990), 865–866  isi]
19. L. M. Lerman, “On the behaviour of a Hamiltonian system in a neighbourhood of the transversal homoclinic orbit of a saddle-focus”, Uspekhi Mat. Nauk, 44:2(266) (1989),  233–234  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:2 (1989), 285–286  isi
20. L. M. Lerman, L. P. Shilnikov, “Homoclinic structures in infinite-dimensional systems”, Sibirsk. Mat. Zh., 29:3 (1988),  92–103  mathnet  mathscinet  zmath; Siberian Math. J., 29:3 (1988), 408–417  isi
21. L. M. Lerman, Ya. L. Umanskii, “Necessary conditions for the existence of heteroclinic trajectories in an integral Hamiltonian system with two degrees of freedom”, Uspekhi Mat. Nauk, 38:5(233) (1983),  195–196  mathnet  mathscinet  zmath; Russian Math. Surveys, 38:5 (1983), 150–151  isi
22. A. G. Vainshtein, L. M. Lerman, “Uniform structures and the equivalence of diffeomorphisms”, Mat. Zametki, 23:5 (1978),  739–752  mathnet  mathscinet  zmath; Math. Notes, 23:5 (1978), 407–414
23. A. G. Vainshtein, L. M. Lerman, “Nonautonomous suspensions over diffeomorphisms, and the geometry of nearness”, Uspekhi Mat. Nauk, 31:5(191) (1976),  231–232  mathnet  mathscinet  zmath
24. L. M. Lerman, L. P. Shilnikov, “On the classification of structurally stable nonautonomous systems of second order with a finite number of cells”, Dokl. Akad. Nauk SSSR, 209:3 (1973),  544–547  mathnet  mathscinet  zmath

25. S. V. Gonchenko, E. V. Zhuzhoma, E. Ya. Gurevich, L. M. Lerman, O. V. Pochinka, V. F. Tishkin, I. I. Chuchaev, L. A. Sukharev, P. A. Shamanaev, R. V. Zhalnin, T. Ph. Mamedova, “Вячеслав Зигмундович Гринес (к семидесятилетию со дня рождения)”, Zhurnal SVMO, 18:4 (2016),  168–171  mathnet
26. V. S. Afraimovich, L. A. Belyakov, V. V. Bykov, S. V. Gonchenko, L. M. Lerman, V. I. Lukyanov, M. I. Malkin, A. D. Morozov, D. V. Turaev, “Leonid Pavlovich Shilnikov (17.12.1934–26.12.2011)”, Nelin. Dinam., 8:1 (2012),  183–186  mathnet
27. D. V. Anosov, V. S. Afraimovich, L. A. Bunimovich, S. V. Gonchenko, V. Z. Grines, Yu. S. Ilyashenko, A. B. Katok, S. A. Kashchenko, V. V. Kozlov, L. M. Lerman, A. D. Morozov, A. I. Neishtadt, Ya. B. Pesin, A. M. Samoilenko, Ya. G. Sinai, D. V. Treschev, D. V. Turaev, A. N. Sharkovskii, A. L. Shil'nikov, “Leonid Pavlovich Shil'nikov (obituary)”, Uspekhi Mat. Nauk, 67:3(405) (2012),  175–178  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 67:3 (2012), 573–577  isi
28. V. S. Afraimovich, L. M. Lerman, S. V. Gonchenko, “Leonid Pavlovich Shilnikov (to the 75th anniversary)”, Nelin. Dinam., 6:1 (2010),  5–22  mathnet
29. L. Lerman, “Breaking hyperbolicity for smooth symplectic toral diffeomorphisms”, Regul. Chaotic Dyn., 15:2-3 (2010),  194–209  mathnet  mathscinet  zmath
30. L. M. Lerman, A. P. Markova, “On Stability at the Hamiltonian Hopf Bifurcation”, Regul. Chaotic Dyn., 14:1 (2009),  148–162  mathnet  mathscinet  zmath
31. S. V. Gonchenko, L. M. Lerman, D. V. Turaev, “Leonid Pavlovich Shilnikov. On his 70th birthday”, Regul. Chaotic Dyn., 11:2 (2006),  139–140  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Неавтономные векторные поля на замкнутых многообразиях: структурная устойчивость, инварианты и реализация
L. M. Lerman

August 10, 2021 15:10
2. Некоторые задачи теории бифуркаций интегрируемых систем
L. M. Lerman
Differential geometry and applications
May 13, 2019 16:45
3. Неинтегрируемые системы и гомоклиническая динамика
L. M. Lerman
Modern geometry methods
November 28, 2018 18:30
4. On skew products over a quasi–periodic shift of the circle
L. M. Lerman
International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko
November 27, 2018 15:30   
5. Nonautonomous dynamics: Anosov's heritage in action
Lev Lerman
International Conference “Anosov Systems and Modern Dynamics” dedicated to the 80th anniversary of Dmitry Anosov
December 19, 2016 17:00   
6. 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
7. On dynamics of slow varying Duffing-type system
N. E. Kulagin, L. M. Lerman
International Conference on Differential Equations and Dynamical Systems
July 6, 2014 10:50

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