Persons: Lerman, Lev Mikhailovich

Persons

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

Lerman, Lev Mikhailovich

Statistics
in MathSciNet:	34 (28)
in zbMATH:	31 (26)
in Web of Science:	16 (14)
in Scopus:	9 (9)

Professor

Doctor of physico-mathematical sciences (1999)

Speciality:

01.01.02 (Differential equations, dynamical systems, and optimal control)

E-mail:

Keywords:

Hamiltonian, homoclinic, symplectic, nonautonomous, bifurcation.

Subject:

Dynamical Systems.

Main publications:

L. M. Lerman, L. P. Shilnikov, “O klassifikatsii grubykh neavtonomnykh sistem vtorogo poryadka s konechnym chislom yacheek”, DAN SSSR, 209:3 (1973), 544–547
L. M. Lerman, L. P. Shilnikov, “Gomoklinicheskie struktury v beskonechnomernykh sistemakh”, Sib. matem. zhurn., 29:3 (1988), 408–417
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
L. M. Lerman, L. P. Shil'nikov, “Homoclinical Structures in Nonautonomous Systems: Nonautonomous Chaos”, Chaos: Interdisc. J. Nonlinear Sci., 2:3, 447–454
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
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
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
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
V. Gelfreich, L. M. Lerman, “Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system”, Nonlinearity, 15 (2002), 447–457
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
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
L. M. Lerman, “Remarks on skew products over irrational rotations”, International Journal of Bifurcation and Chaos, 15 (2005), 3675–3689

https://www.mathnet.ru/eng/person8363

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/212730

https://elibrary.ru/author_items.asp?authorid=106647

Full list of publications:

Download file (191 kB)

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	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”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 511–542
2.	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	39 ^[x]
3.	V. Gelfreich, L. M. Lerman, “Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system”, Nonlinearity, 15 (2002), 447–457	39 ^[x]
4.	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	34 ^[x]
5.	L. M. Lerman, L. P. Shil'nikov, “Homoclinical Structures in Nonautonomous Systems: Nonautonomous Chaos”, Chaos: Interdisc. J. Nonlinear Sci., 2:3 (1992), 447–454 (to appear)	30 ^[x]
6.	Lev M. Lerman, Dimitry Turaev, “Breakdown of Symmetry in Reversible Systems”, Regul. Chaotic Dyn., 17:3-4 (2012), 318–336	24 ^[x]
7.	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”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 479–506
8.	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	18 ^[x]
9.	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”, JETP Letters, 110:7 (2019), 481–486
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	14 ^[x]
11.	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”, Sb. Math., 186:10 (1995), 1477–1491
12.	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	10 ^[x]
13.	Vassili Gelfreich, Lev Lerman, “Separatrix Splitting at a Hamiltonian $0^2 i\omega$ Bifurcation”, Regul. Chaotic Dyn., 19:6 (2014), 635–655	9 ^[x]
14.	N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “On Radial Solutions of the Swift–Hohenberg Equation”, Proc. Steklov Inst. Math., 261 (2008), 183–203
15.	N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “Fronts, traveling fronts, and their stability in the generalized Swift–Hohenberg equation”, Comput. Math. Math. Phys., 48:4 (2008), 659–676
16.	L. M. Lerman, L. P. Shilnikov, “Homoclinic structures in infinite-dimensional systems”, Siberian Math. J., 29:3 (1988), 408–417
17.	L.M. Lerman, P.E. Naryshkin, A.I. Nazarov, “Abundance of entire solutions to nonlinear elliptic equations by the variational method”, Nonlinear Analysis: theory, methods, and applications, 190 (2020), 111590 , 21 pp.	6 ^[x]
18.	L. M. Lerman, “Remarks on skew products over irrational rotations”, International Journal of Bifurcation and Chaos, 15 (2005), 3675–3689	5 ^[x]
19.	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	5 ^[x]
20.	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
21.	V. Z. Grines, L. M. Lerman, “Nonautonomous vector fields on $S^3$: Simple dynamics and wild embedding of separatrices”, Theoret. and Math. Phys., 212:1 (2022), 903–917
22.	N. Kulagin, L. Lerman, A. Malkin, “Solitons and cavitons in a nonlocal Whitham equation”, Communications in Nonlinear Science and Numerical Simulation, 93, February (2021), 105525	4 ^[x]
23.	L. Lerman, E. Yakovlev, “On interrelations between divergence-free and Hamiltonian dynamics”, J. Geometry and Physics, 135 (2019), 70-79	4 ^[x]
24.	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	4 ^[x]
25.	A. G. Vainshtein, L. M. Lerman, “Uniform structures and the equivalence of diffeomorphisms”, Math. Notes, 23:5 (1978), 407–414
26.	E. A. Kudryavtseva, L. M. Lerman, “Bifurcations in Integrable Systems with Three Degrees of Freedom. I”, Proc. Steklov Inst. Math., 327 (2024), 130–207
27.	L.M. Lerman, K.N. Trifonov, “Saddle-center and periodic orbit: dynamics near symmetric heteroclinic connection”, Chaos, 31 (2021), 023113	3 ^[x]
28.	L.M. Lerman, K.N. Trifonov, “Geometry of symplectic partially hyperbolic automorphisms on 4-torus”, Dynamical Systems, 35:4 (2020), 609-624	3 ^[x]
29.	L. M. Lerman, D. V. Turaev, “O bifurkatsiyakh poteri simmetrii v obratimykh sistemakh”, Nelineinaya dinam., 8:2 (2012), 323–343	3 ^[x]
30.	L. M. Lerman, Ya. L. Umanskii, “Necessary conditions for the existence of heteroclinic trajectories in an integral Hamiltonian system with two degrees of freedom”, Russian Math. Surveys, 38:5 (1983), 150–151
31.	A. G. Vainshtein, L. M. Lerman, “Nonautonomous suspensions over diffeomorphisms, and the geometry of nearness”, Uspekhi Mat. Nauk, 31:5(191) (1976), 231–232
32.	N.E.Kulagin, L.M. Lerman, “On periodically modulated rolls in the generalized Swift-Hohenberg equation: Galerkin' approximations”, Physica D: Nonlinear Phenomena, 454 (2023), 133845	2 ^[x]
33.	V. Z. Grines, L. M. Lerman, “Nonautonomous dynamics: classification, invariants, and implementation”, Differential and functional differential equations, CMFD, 68, no. 4, PFUR, M., 2022, 596–620
34.	L. M. Lerman, K. N. Trifonov, “The Topology of Symplectic Partially Hyperbolic Automorphisms of the 4-Torus”, Math. Notes, 108:3 (2020), 462–464
35.	L.M. Lerman, E.V. Gubina, “Nonautonomous gradient-like ODEs on the circle: classification, structural stability and autonomization”, Discr. Cont. Dynam. Syst., Ser. S, 13:4 (2020), 1341-1367	2 ^[x]
36.	Trans. Moscow Math. Soc., 76:2 (2015), 271–299
37.	L. M. Lerman, Ya. L. Umanskii, “Isoenergetic classification of integrable Hamiltonian systems in a neighborhood of a simple elliptic point”, Math. Notes, 55:5 (1994), 496–501
38.	Nikolay E. Kulagin, Lev M. Lerman, Konstantin N. Trifonov, “Twin Heteroclinic Connections of Reversible Systems”, Regul. Chaotic Dyn., 29:1 (2024), 40–64	1 ^[x]
39.	L.M. Lerman, K.N. Trifonov, “Symplectic partially hyperbolic automorphisms of 6-torus”, Journal of Geometry and Physics, 195 (2024), 105038	1 ^[x]
40.	V. Z. Grines, L. M. Lerman, “Gradient-like diffeomorphisms and periodic vector fields”, Mosc. Math. J., 23:4 (2023), 533–544	1 ^[x]
41.	E. G. Galkina, B. A. Ivanov , N. E. Kulagin, L. M. Lerman, I. A. Yastremskii, “Dinamika domennykh stenok v kiralnykh magnetikakh”, ZhETF, 159:4 (2021), 1-16	1 ^[x]
42.	E. G. Galkina, B. A. Ivanov , N. E. Kulagin, L. M. Lerman, I. A. Yastremskii, “Dinamika domennykh stenok v kiralnykh magnetikakh”, ZhETF, 159:4 (2021), 1-16	1 ^[x]
43.	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”, Journal of Mathematical Sciences, 202:5 (2014), 684–702
44.	L. M. Lerman, N. A. Slinyakova, “O dinamike kusochno-lineinoi modeli uravneniya Svifta–Khoenberga”, Nelineinaya dinam., 5:4 (2009), 569–583	1 ^[x]
45.	L. M. Lerman, “On the behaviour of a Hamiltonian system in a neighbourhood of the transversal homoclinic orbit of a saddle-focus”, Russian Math. Surveys, 44:2 (1989), 285–286
46.	Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov. Part II. Homoclinic Chaos”, Regul. Chaotic Dyn., 30:2 (2025), 155–173
47.	L. M. Lerman, “What I Did in Dynamics”, Rus. J. Nonlin. Dyn., 21:1 (2025), 15–31
48.	L. M. Lerman, V. I. Nekorkin, “V. s. afraimovich: on the 80th anniversary of his birth”, Izvestiya VUZ. Applied Nonlinear Dynamics, 33:4 (2025), 431–434
49.	Kolonitsky S.B., Lerman L.M., Nazarov A.I., “Entire solutions to the Swift-Hohenberg equation via a variational approach”, Calc. of Var. and Partial Diff. Equat., 64:5 (2025), 149
50.	N. E. Kulagin, L. M. Lerman, “Spatial dynamics in the family of sixth-order differential equations from the theory of partial formation”, Izvestiya VUZ. Applied Nonlinear Dynamics, 32:6 (2024), 878–896
51.	Grines V.Z., Lerman L.M., “Nonautonomous Dynamics: Classification, Invariants, and Implementation”, J. Math. Sci. , 283:1 (2024), 40-62
52.	A. Gevorgian, N. Kulagin, L. Lerman, A. Malkin, “Solitons of Whitham equation with resonance dispersion”, Chaos, Solitons and Fractals, 143 (2021), 110550
53.	L. M. Lerman, “Partial normal form near a saddle of a Hamiltonian system”, Regul. Chaotic Dyn., 11:2 (2006), 291–297
54.	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
55.	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”, Sov J Quantum Electron, 20:7 (1990), 865–866
56.	L. M. Lerman, A. P. Markova, “On Stability at the Hamiltonian Hopf Bifurcation”, Regul. Chaotic Dyn., 14:1 (2009), 148–162	20 ^[x]
57.	L. Lerman, “Breaking hyperbolicity for smooth symplectic toral diffeomorphisms”, Regul. Chaotic Dyn., 15:2-3 (2010), 194–209	3 ^[x]
58.	O. N. Ageev, Ya. B. Vorobets, B. Weiss, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, L. S. Efremova, A. Yu. Zhirov, E. V. Zhuzhoma, B. S. Kashin, V. N. Kolokoltsov, A. V. Kochergin, L. M. Lerman, I. V. Mykytyuk, V. I. Oseledets, A. Yu. Plakhov, O. V. Pochinka, V. V. Ryzhikov, V. Zh. Sakbaev, A. G. Sergeev, Ya. G. Sinai, A. T. Tagi-Zade, S. V. Tikhonov, J.-P. Thouvenot, A. Ya. Helemskii, A. I. Shafarevich, “Anatolii Mikhailovich Stepin (obituary)”, Russian Math. Surveys, 77:2 (2022), 361–367
59.	O. V. Anashkin, P. M. Akhmet'ev, D. V. Balandin, M. K. Barinova, I. V. Boykov, A. N. Bezdenezhnyh, V. N. Belykh, P. A. Vel'misov, I. Yu. Vlasenko, O. E. Galkin, S. Yu. Galkina, V. K. Gorbunov, S. D. Glyzin, S. V. Gonchenko, A. S. Gorodetski, E. V. Gubina, E. Ya. Gurevich, A. A. Davydov, L. S. Efremova, R. V. Zhalnin, A. Yu. Zhirov, E. V. Zhuzhoma, N. I. Zhukova, S. Kh. Zinina, Yu. S. Ilyashenko, N. V. Isaenkova, A. O. Kazakov, A. V. Klimenko, S. A. Komech, Yu. A. Kordyukov, V. E. Kruglov, E. V. Kruglov, E. B. Kuznetsov, S. K. Lando, Yu. A. Levchenko, L. M. Lerman, S. I. Maksimenko, M. I. Malkin, D. S. Malyshev, V. K. Mamaev, T. Ph. Mamedova, V. S. Medvedev, T. V. Medvedev, D. I. Mints, T. M. Mitryakova, A. D. Morozov, A. I. Morozov, E. V. Nozdrinova, E. N. Pelinovsky, Ya. B. Pesin, A. S. Pikovsky, S. Yu. Pilyugin, G. M. Polotovsky, O. V. Pochinka, I. D. Remizov, P. E. Ryabov, A. S. Skripchenko, A. V. Slunyaev, S. V. Sokolov, L. A. Sukharev, E. A. Talanova, V. A. Timorin, S. B. Tikhomir, “To the 75th anniversary of Vyacheslav Zigmundovich Grines”, Zhurnal SVMO, 23:4 (2021), 472–476
60.	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, Zhurnal SVMO, 18:4 (2016), 168–171
61.	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)”, Nelineinaya dinam., 8:1 (2012), 183–186
62.	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)”, Russian Math. Surveys, 67:3 (2012), 573–577
63.	V. S. Afraimovich, L. M. Lerman, S. V. Gonchenko, “Leonid Pavlovich Shilnikov: K 75-letiyu so dnya rozhdeniya”, Nelineinaya dinam., 6:1 (2010), 5–22
64.	S. V. Gonchenko, L. M. Lerman, D. V. Turaev, “Leonid Pavlovich Shilnikov. On his 70th birthday”, Regul. Chaotic Dyn., 11:2 (2006), 139–140

Presentations in Math-Net.Ru

1.	Spatial dynamics of some 6th-order ODE from the theory of phase transitions L. M. Lerman Dynamics days in Sirius. On the occasion of academician Dmitry V. Treschev’s anniversary October 29, 2024 10:10
2.	Некоторые методы построения неавтономных систем с заданной динамикой L. M. Lerman Modern geometry methods March 20, 2024 19:00
3.	Симплектические частично-гиперболические автоморфизмы на T6: динамика и классификация L. M. Lerman November 8, 2022 15:00
4.	Hamiltonian homoclinic dynamics L. M. Lerman International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko June 9, 2022 09:30
5.	Неавтономные векторные поля на замкнутых многообразиях: структурная устойчивость, инварианты и реализация L. M. Lerman August 10, 2021 15:10
6.	Некоторые задачи теории бифуркаций интегрируемых систем L. M. Lerman Differential geometry and applications May 13, 2019 16:45
7.	Неинтегрируемые системы и гомоклиническая динамика L. M. Lerman Modern geometry methods November 28, 2018 18:30
8.	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
9.	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
10.	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
11.	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

Organisations