Persons: Bolotin Sergey Vladimirovich, List of publications

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Bolotin Sergey Vladimirovich

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2026
1.	Sergey V. Bolotin, Dmitry V. Treschev, “Erratum to: On the Problem of Stability of Viscous Shocks”, Regul. Chaotic Dyn., 31:1 (2026), 173 ;

2025
2.	Sergey V. Bolotin, “Dynamics of Slow-Fast Hamiltonian Systems: The Saddle–Focus Case”, Regul. Chaotic Dyn., 30:1 (2025), 76–92	1 ^[x]
3.	S. Bolotin, “Chaotic dynamics for the two-body problem on a sphere”, Chaos, 35:8 (2025), 083134, 6 pp.	2 ^[x]
4.	S.V. Bolotin, D.V. Treschev, “On the Problem of Stability of Viscous Shocks”, Regul. Chaot. Dyn., 30:6 (2025), 908–930
5.	S. V. Bolotin, O. È. Zubelevich, V. V. Kozlov, S. B. Kuksin, A. I. Neishtadt, “Dmitry Valerievich Treschev (on his sixtieth birthday)”, Russian Math. Surveys, 80:1 (2025), 155–160

2024
6.	S. Bolotin, D. Treschev, “Another billiard problem”, Russ. J. Math. Phys., 31:1 (2024), 50–59	9 ^[x]
7.	D. V. Treschev, E. I. Kugushev, T. V. Popova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskii, “Kafedra teoreticheskoi mekhaniki i mekhatroniki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 103–113
8.	S. V. Bolotin, A. T. Il'ichev, V. V. Kozlov, D. V. Treshchev, A. P. Chugainova, “Andrei Gennad'evich Kulikovskii (obituary)”, Russian Math. Surveys, 79:5 (2024), 919–921

2023
9.	Sergey V. Bolotin, Dmitry V. Treschev, “Quasiperiodic Version of Gordon’s Theorem”, Regul. Chaotic Dyn., 28:1 (2023), 5–13	2 ^[x]
10.	Sergey V. Bolotin, “Separatrix Maps in Slow–Fast Hamiltonian Systems”, Proc. Steklov Inst. Math., 322 (2023), 32–51

2021
11.	Ivan Bizyaev, Sergey Bolotin, Ivan Mamaev, “Normal forms and averaging in an acceleration problem in nonholonomic mechanics”, Chaos, 31:1 (2021), 013132, 28 pp.	9 ^[x]
12.	Sergey Bolotin, “Shadowing Homoclinic Chains to a Symplectic Critical Manifold”, Anal. Theory Appl., 37:1 (2021), 1–23	1 ^[x]
13.	S. V. Bolotin, “Crossing of the Critical Energy Level in Hamiltonian Systems with Slow Dependence on Time”, Math. Notes, 110:6 (2021), 956–959

2020
14.	Sergey V. Bolotin, “Local Adiabatic Invariants Near a Homoclinic Set of a Slow–Fast Hamiltonian System”, Proc. Steklov Inst. Math., 310 (2020), 12–24
15.	Izbrannye voprosy matematiki i mekhaniki, Sbornik statei. K 70-letiyu so dnya rozhdeniya akademika Valeriya Vasilevicha Kozlova, Trudy MIAN, 310, ed. D. V. Treschev, S. V. Bolotin, A. G. Kulikovskii, I. A. Taimanov, MIAN, M., 2020, 341 pp.
16.	A. V. Artem'ev, S. V. Bolotin, D. L. Vainchtein, A. A. Vasiliev, S. Yu. Dobrokhotov, L. M. Zelenyi, V. V. Kozlov, A. A. Petrukovich, V. V. Sidorenko, D. V. Treschev, A. I. Shafarevich, “Anatolii Iserovish Neishtadt (on his 70th birthday)”, Russian Math. Surveys, 75:5 (2020), 981–989
17.	S. V. Bolotin, A. V. Borisov, A. V. Karapetyan, B. S. Kashin, E. I. Kugushev, A. I. Neishtadt, D. O. Orlov, D. V. Treschev, “Valerii Vasil'evich Kozlov (on his 70th birthday)”, Russian Math. Surveys, 75:6 (2020), 1165–1180

2019
18.	Sergey V. Bolotin, “Jumps of Energy Near a Homoclinic Set of a Slowly Time Dependent Hamiltonian System”, Regul. Chaotic Dyn., 24:6 (2019), 682–703	4 ^[x]

2018
19.	S. V. Bolotin, “Jumps of energy near a separatrix in slow-fast Hamiltonian systems”, Russian Math. Surveys, 73:4 (2018), 725–727

2017
20.	Sergey V. Bolotin, “Degenerate Billiards in Celestial Mechanics”, Regul. Chaotic Dyn., 22:1 (2017), 27–53	9 ^[x]
21.	S. V. Bolotin, V. V. Kozlov, “Topological approach to the generalized $n$-centre problem”, Russian Math. Surveys, 72:3 (2017), 451–478
22.	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

2016
23.	S. V. Bolotin, “Degenerate billiards”, Proc. Steklov Inst. Math., 295 (2016), 45–62

2015
24.	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
25.	S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030

2014
26.	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	7 ^[x]

2013
27.	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	8 ^[x]
28.	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	12 ^[x]
29.	S. Bolotin, P. Negrini, “Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system”, Regul. Chaotic Dyn., 18:6 (2013), 774–800	7 ^[x]
30.	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
31.	S. V. Bolotin, “Zadacha optimalnogo upravleniya kacheniem shara s rotorami”, Nelineinaya dinam., 8:4 (2012), 837–852	4 ^[x]
32.	S. V. Bolotin, “The problem of optimal control of a Chaplygin ball by internal rotors”, Regul. Chaotic Dyn., 17:6 (2012), 559–570	17 ^[x]

2011
33.	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	2 ^[x]

2010
34.	S. V. Bolotin, D. V. Treschev, “Hill's formula”, Russian Math. Surveys, 65:2 (2010), 191–257
35.	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
36.	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
37.	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
38.	S. V. Bolotin, A. V. Karapetyan, E. I. Kugushev, D. V. Treschev, Teoreticheskaya mekhanika, Izd-vo «Akademiya», Moskva, 2010, 432 pp.

2007
39.	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	8 ^[x]

2006
40.	S. Bolotin, “Symbolic dynamics of almost collision orbits and skew products of symplectic maps”, Nonlinearity, 19:9 (2006), 2041–2063	24 ^[x]
41.	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	19 ^[x]
42.	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	6 ^[x]
43.	S. Bolotin, “Shadowing chains of collision orbits”, Discrete Contin. Dyn. Syst., 14:2 (2006), 235–260	13 ^[x]

2005
44.	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	1 ^[x]
45.	S. Bolotin, “Second species periodic orbits of the elliptic 3 body problem”, Celestial Mech. Dynam. Astronom., 93:1-4 (2005), 343–371	11 ^[x]

2004
46.	S. Bolotin, A. Delshams, R. Ramírez-Ros, “Persistence of homoclinic orbits for billiards and twist maps”, Nonlinearity, 17:4 (2004), 1153–1177	8 ^[x]

2003
47.	M. L. Bertotti, S. V. Bolotin, “Chaotic trajectories for natural systems on a torus”, Discrete Contin. Dyn. Syst., 9:5 (2003), 1343–1357	2 ^[x]
48.	S. V. Bolotin, P. Negrini, “Chaotic behavior in the 3-center problem”, J. Differential Equations, 190:2 (2003), 539–558	13 ^[x]
49.	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	23 ^[x]

2002
50.	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
51.	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	4 ^[x]
52.	S. Bolotin, P. Negrini, “Global regularization for the $n$-center problem on a manifold”, Discrete Contin. Dyn. Syst., 8:4 (2002), 873–892	8 ^[x]

2001
53.	S. V. Bolotin, “Symbolic dynamics near minimal hyperbolic invariant tori of Lagrangian systems”, Nonlinearity, 14:5 (2001), 1123–1140	7 ^[x]
54.	S. V. Bolotin, P. Negrini, “Regularization and topological entropy for the spatial $n$-center problem”, Ergodic Theory Dynam. Systems, 21:2 (2001), 383–399	16 ^[x]

2000
55.	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
56.	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	39 ^[x]
57.	S. V. Bolotin, D. V. Treschev, “Remarks on the definition of hyperbolic tori of Hamiltonian systems”, Regul. Chaotic Dyn., 5:4 (2000), 401–412	28 ^[x]
58.	S. V. Bolotin, “Infinite number of homoclinic orbits to hyperbolic invariant tori of Hamiltonian systems”, Regul. Chaotic Dyn., 5:2 (2000), 139–156	6 ^[x]
59.	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	3 ^[x]

1999
60.	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
61.	S. V. Bolotin, P. H. Rabinowitz, “Minimal heteroclinic geodesics for the $n$-torus”, Calc. Var. Partial Differential Equations, 9:2 (1999), 125–139	3 ^[x]
62.	S. Bolotin, D. Treschev, “Unbounded growth of energy in nonautonomous Hamiltonian systems”, Nonlinearity, 12:2 (1999), 365–388	54 ^[x]

1998
63.	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	5 ^[x]
64.	S. V. Bolotin, P. H. Rabinowitz, “Heteroclinic geodesics for a class of manifolds with symmetry”, Regul. Chaotic Dyn., 3:4 (1998), 49–62	2 ^[x]
65.	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
66.	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
67.	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
68.	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	21 ^[x]

1997
69.	S. Bolotin, P. Negrini, “A variational criterion for nonintegrability”, Russian J. Math. Phys., 5:4 (1997), 415–436
70.	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
71.	S. Bolotin, R. MacKay, “Multibump orbits near the anti-integrable limit for Lagrangian systems”, Nonlinearity, 10:5 (1997), 1015–1029	25 ^[x]
72.	S. Bolotin, “Homoclinic trajectories of invariant sets of Hamiltonian systems”, NoDEA Nonlinear Differential Equations Appl., 4:3 (1997), 359–389	7 ^[x]

1995
73.	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
74.	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
75.	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	10 ^[x]
76.	S. V. Bolotin, V. V. Kozlov, “Symmetry fields of geodesic flows”, Russian J. Math. Phys., 3:3 (1995), 279–295
77.	S. Bolotin, P. Negrini, “Asymptotic solutions of Lagrangian systems with gyroscopic forces”, NoDEA Nonlinear Differential Equations Appl., 2:4 (1995), 417–444	13 ^[x]
78.	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
79.	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
80.	M. L. Bertotti, S. V. Bolotin, “Homoclinic solutions of quasiperiodic Lagrangian systems”, Differential Integral Equations, 8:7 (1995), 1733–1760

1994
81.	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

1993
82.	S. V. Bolotin, P. Negrini, “Asimptoticheskie traektorii giroskopicheskikh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1993, no. 6, 66–75
83.	S. V. Bolotin, “Homoclinic orbits of geodesic flows on surfaces”, Russian J. Math. Phys., 1:3 (1993), 275–288

1992
84.	S. V. Bolotin, “Dvoyakoasimptoticheskie traektorii minimalnykh geodezicheskikh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1992, no. 1, 92–96	4 ^[x]
85.	S. V. Bolotin, “Homoclinic trajectories to minimal tori of Lagrangian systems”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1992, no. 6, 34–41
86.	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
87.	S. V. Bolotin, “Integrable billiards on surfaces of constant curvature”, Math. Notes, 51:2 (1992), 117–123
88.	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
89.	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
90.	S. V. Bolotin, “Integriruemye bilyardy Birkgofa”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1990, no. 2, 33–36	15 ^[x]
91.	S. V. Bolotin, “Dvoyakoasimptoticheskie traektorii i usloviya integriruemo sti gamiltonovykh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1990, no. 1, 55–63	3 ^[x]

1988
92.	S. V. Bolotin, “O pervykh integralakh sistem s uprugimi otrazheniyami”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1988, no. 6, 42–45	3 ^[x]
93.	S. V. Bolotin, “Ob opredelitele Khilla periodicheskoi traektorii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1988, no. 3, 30–34	3 ^[x]

1987
94.	S. V. Bolotin, “Periodic solutions of systems with gyroscopic forces”, J. Appl. Math. Mech., 51:4 (1987), 535–537

1986
95.	S. V. Bolotin, “The splitting of asymptotic surfaces”, Geometriya, differentsialnye uravneniya i mekhanika (Moskva, 1985), Izd-vo MGU, M., 1986, 52–53
96.	S. V. Bolotin, “Zamechanie o metode Rausa i gipoteze Gertsa”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1986, no. 5, 51–53	2 ^[x]
97.	S. V. Bolotin, “Uslovie neintegriruemosti po Liuvillyu gamiltonovykh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1986, no. 3, 58–64	1 ^[x]

1984
98.	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
99.	S. V. Bolotin, “O pervykh integralakh sistem s giroskopicheskimi silami”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1984, no. 6, 75–82	10 ^[x]
100.	S. V. Bolotin, “Neintegriruemost zadachi $n$ tsentrov pri $n>2$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1984, no. 3, 65–68	11 ^[x]

1983
101.	S. V. Bolotin, “Suschestvovanie gomoklinicheskikh dvizhenii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1983, no. 6, 98–103	1 ^[x]

1980
102.	V. V. Kozlov, S. V. Bolotin, “Ob asimptoticheskikh resheniyakh uravnenii dinamiki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1980, no. 4, 84–89

1978
103.	S. V. Bolotin, V. V. Kozlov, “Libration in systems with many degrees of freedom”, J. Appl. Math. Mech., 42:2 (1978), 256–261
104.	S. V. Bolotin, “Libratsionnye dvizheniya naturalnykh dinamicheskikh si stem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1978, no. 6, 72–77