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
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
2.
L. M. Lerman, “What I Did in Dynamics”, Rus. J. Nonlin. Dyn., 21:1 (2025), 15–31
3.
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
4.
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
2024
5.
Nikolay E. Kulagin, Lev M. Lerman, Konstantin N. Trifonov, “Twin Heteroclinic Connections of Reversible Systems”, Regul. Chaotic Dyn., 29:1 (2024), 40–64
E. A. Kudryavtseva, L. M. Lerman, “Bifurcations in Integrable Systems with Three Degrees of Freedom. I”, Proc. Steklov Inst. Math., 327 (2024), 130–207
7.
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
8.
L.M. Lerman, K.N. Trifonov, “Symplectic partially hyperbolic automorphisms of 6-torus”, Journal of Geometry and Physics, 195 (2024), 105038
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
13.
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
14.
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
2021
15.
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
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
A. Gevorgian, N. Kulagin, L. Lerman, A. Malkin, “Solitons of Whitham equation with resonance dispersion”, Chaos, Solitons and Fractals, 143 (2021), 110550
18.
L.M. Lerman, K.N. Trifonov, “Saddle-center and periodic orbit: dynamics near symmetric heteroclinic connection”, Chaos, 31 (2021), 023113
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
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
2020
21.
L. M. Lerman, K. N. Trifonov, “The Topology of Symplectic Partially Hyperbolic Automorphisms of the 4-Torus”, Math. Notes, 108:3 (2020), 462–464
22.
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
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.
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
26.
L. Lerman, E. Yakovlev, “On interrelations between divergence-free and Hamiltonian dynamics”, J. Geometry and Physics, 135 (2019), 70-79
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
2015
28.
Trans. Moscow Math. Soc., 76:2 (2015), 271–299
2014
29.
Vassili Gelfreich, Lev Lerman, “Separatrix Splitting at a Hamiltonian $0^2 i\omega$ Bifurcation”, Regul. Chaotic Dyn., 19:6 (2014), 635–655
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
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
2012
32.
L. M. Lerman, D. V. Turaev, “O bifurkatsiyakh poteri simmetrii v obratimykh sistemakh”, Nelineinaya dinam., 8:2 (2012), 323–343
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
35.
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
2010
36.
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
37.
L. Lerman, “Breaking hyperbolicity for smooth symplectic toral diffeomorphisms”, Regul. Chaotic Dyn., 15:2-3 (2010), 194–209
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
41.
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
2006
42.
L. M. Lerman, “Partial normal form near a saddle of a Hamiltonian system”, Regul. Chaotic Dyn., 11:2 (2006), 291–297
43.
S. V. Gonchenko, L. M. Lerman, D. V. Turaev, “Leonid Pavlovich Shilnikov. On his 70th birthday”, Regul. Chaotic Dyn., 11:2 (2006), 139–140
2005
44.
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, Ya. L. Umanskiy, Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects), Translations of Mathematical Monographs, 176, AMS, Providence, RI, 1998
1997
49.
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
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, 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
52.
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. 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
54.
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
55.
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
1992
56.
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)
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
58.
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, “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
1988
60.
L. M. Lerman, L. P. Shilnikov, “Homoclinic structures in infinite-dimensional systems”, Siberian Math. J., 29:3 (1988), 408–417
1983
61.
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
1978
62.
A. G. Vainshtein, L. M. Lerman, “Uniform structures and the equivalence of diffeomorphisms”, Math. Notes, 23:5 (1978), 407–414
1976
63.
A. G. Vainshtein, L. M. Lerman, “Nonautonomous suspensions over diffeomorphisms, and the geometry of nearness”, Uspekhi Mat. Nauk, 31:5(191) (1976), 231–232
1973
64.
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
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
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
2025
