Completely integrable Hamiltonian systems,
algebraic separation of variables, bifurcation diagram, bifurcations of
Liouville tori.
Main publications:
M. P. Kharlamov, P. E. Ryabov, “Bifurcations of the first integrals in the Kowalevski–Yehia case”, Regular and Chaotic Dynamics, 2:2 (1997), 25–40
P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, Theoret. and Math. Phys., 134:2 (2003), 181–197
P. E. Ryabov, “Explicit integration and the topology of the D. N. Goryachev case”, Doklady Mathematics, 84:1 (2011), 502–505
M. P. Kharlamov, P. E. Ryabov, “Net Diagrams for the Fomenko Invariant in the Integrable System with
Three Degrees of Freedom”, Doklady Mathematics, 86:3 (2012), 839–842
P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics
of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015
Pavel E. Ryabov, Sergei V. Sokolov, “Bifurcation Diagram of the Model of a Lagrange Top with a Vibrating Suspension Point”, Mathematics, 11:3 (2023), 533 (Published online)
P. E. Ryabov, S. V. Sokolov, “Bifurkatsionnaya diagramma odnoi modeli volchka Lagranzha s vibriruyuschei tochkoi podvesa”, Ustoichivost i kolebaniya nelineinykh sistem upravleniya (konferentsiya Pyatnitskogo). Materialy XVI Mezhdunarodnoi nauchnoi konferentsii. (Moskva, 01–03 iyunya 2022 goda), eds. Pod obschei redaktsiei V. N. Tkhai., Institut problem upravleniya im. V.A. Trapeznikova RAN (Moskva), Moskva, 2022, 381–384
3.
P. E. Ryabov, S. V. Sokolov, “Bifurkatsii pervykh integralov v odnoi modeli volchka Lagranzha s vibriruyuschei tochkoi podvesa”, Sovremennye metody teorii kraevykh zadach. Materialy Mezhdunarodnoi konferentsii. Voronezhskaya vesennya matematicheskaya shkola. Pontryaginskie chteniya - XXXIII (Voronezh, 03–09 maya 2022 goda), Voronezhskii gosudarstvennyi universitet (Voronezh), Voronezh, 2022, 241–242
4.
P. E. Ryabov, S. V. Sokolov, “Phase topology of one model of a Lagrange top with a vibrating suspension point”, Mezhdunarodnaya konferentsiya po differentsialnym uravneniyam i dinamicheskim sistemam (Suzdal, 30 iyunya-05 iyulya 2022 g.), eds. Kozlov V.V., Treschev D.V., Davydov A.A., OOO “Arkaim”, Suzdal, 2022, 61–62
2021
5.
Pavel E. Ryabov, Sergei V. Sokolov, Gleb P. Palshin, Dynamics of a few vortices in an ideal fluid and in a Bose-Einstein condensate, 2021 (Published online) , 14 pp., arXiv: 2103.11667
6.
Gleb P. Palshin, Pavel E. Ryabov, Sergei V. Sokolov, “Can a bifurcation diagram contain loops?”, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), International Conference “Nonlinearity, Information and Robotics” (NIR), 2021 (Innopolis, Russian Federation, 26-29 Aug. 2021), IEEE, 2021, 94-97https://ieeexplore.ieee.org/document/9666072
P.E. Ryabov, S.V. Sokolov and G.P. Palshin, “New Bifurcation Diagram in One Generalized Model of the Vortex Dynamics”, International Conference “Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis” Book Abstract (June 30–July 9, 2021, Moscow Region, Dolgoprudny), Obschestvo s ogranichennoi otvetstvennostyu MESOL, Moscow, 2021, 151-153http://www.mathnet.ru/supplement/conf/1918/Abstracts-MPDSIDA2021.pdf
8.
O. V. Anashkin, P. M. Akhmet'ev, D. V. Balandin, M. K. Barinova, I. V. Boykov, 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, 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. Tikhomirov, V. F. Tishkin, D. V. Treschev, D. , “To the 75th anniversary of Vyacheslav Zigmundovich Grines”, Zhurnal SVMO, 23:4 (2021), 472–476
2020
9.
A. V. Borisov, P. E. Ryabov, S. V. Sokolov, “On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point”, Dokl. Math., 102:3 (2020), 468–471
2019
10.
P. E. Ryabov, S. V. Sokolov, Nelin. Dinam., 15:1 (2019), 59–66
11.
P. E. Ryabov, “Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose–Einstein condensate”, Dokl. Math., 99:2 (2019), 225–229
12.
Pavel E. Ryabov, Artemiy A. Shadrin, “Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics”, Regul. Chaotic Dyn., 24:4 (2019), 418–431
S. V. Sokolov, P. E. Ryabov, “Bifurcation Diagram of the Two Vortices in a Bose–Einstein Condensate with Intensities of the Same Signs”, Doklady Mathematics, 97:3 (2018), 286–290
14.
P. E. Ryabov, Bifurcation diagram of one perturbed vortex dynamics problem, 2018 , 10 pp., arXiv: 1811.10512
15.
P. E. Ryabov, On one unstable bifurcation in the dynamics of vortex structure, 2018 , 11 pp., arXiv: 1812.03563
16.
P. E. Ryabov, S. V. Sokolov, Phase Topology of Two Vortices of the Identical Intensities in Bose-Einstein Condensate, 2018 , 9 pp., arXiv: 1812.11749
17.
P. E. Ryabov, S. V. Sokolov, “Topological atlas of integrable problems of rigid body dynamics”, International Scientific Conference “INTEGRABLE SYSTEMS AND NONLINEAR DYNAMICS”, ABSTRACTS (Yaroslavl, October 1–5, 2018), ISBN: 978-5-8397-1156-3, Yaroslavskii gosudarstvennyi universitet im. P.G. Demidova, 2018, 73-74
2017
18.
Ryabov P. E., “Explicit Integration of the System of Invariant Relations for the Case of M. Adler and P. van Moerbeke”, Doklady Mathematics, 95:1 (2017), 17–20
19.
Kharlamov M. P., Ryabov P. E., Kharlamova I. I., “Topological Atlas of the Kovalevskaya–Yehia Gyrostat”, Journal of Mathematical Sciences (United States), 227:3 (2017), 241–386
A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russian Journal of Mathematical Physics, 24:4 (2017), 517–525
21.
P. E. Ryabov, S. V. Sokolov, “Separation of variables for integrable case of the Kowalevski top in a non-Euclidean space”, The International Scientific Workshop “Recent Advances in Hamiltonian and Nonholonomic Dynamics”, Book of Abstracts, (Moscow Institute of Physics and Technology (Dolgoprudny), Russia, 15 -18 june 2017), Moscow-Izhevsk: Publishing Center “Institute of Computer Science”, Izhevsk, 2017, 65 - 66
22.
P. E. Ryabov, S. V. Sokolov, “Novye invariantnye sootnosheniya odnoi kriticheskoi podsistemy dlya obobschennogo dvukhpolevogo girostata”, Mezhdunarodnaya konferentsiya po matematicheskoi teorii upravleniya i mekhanike (Suzdal, 7- 11 iyulya 2017 g.), Tezisy dokladov, Vladimir: OOO “Arkaim”, 2017, 121-122
23.
Sergei V. Sokolov, Pavel E. Ryabov, “Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs”, Regul. Chaotic Dyn., 22:8 (2017), 976–995
A. V. Borisov, P. E. Ryabov, S. V. Sokolov, “Bifurcation Analysis of the Motion of a Cylinder and a Point Vortex in an Ideal Fluid”, Math. Notes, 99:6 (2016), 834–839
25.
Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592 , 12 pp.
P. E. Ryabov, E. O. Birucheva, “The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke”, Nelin. Dinam., 12:4 (2016), 633–650
2017
28.
M. P. Kharlamov, P. E. Ryabov, I. I. Kharlamova, “Topological Atlas of the Kovalevskaya–Yehia Gyrostat”, J. Math. Sci. (N. Y.), 227:3 (2017), 241–386
2016
29.
P. E. Ryabov, “Uravneniya Abelya - Yakobi dlya integriruemogo sluchaya Kovalevskoi-Yakhya v dinamike tverdogo tela pri nulevoi postoyannoi ploschadei”, Programma 59-i nauchnoi konferentsii MFTI s mezhdunarodnym uchastiem. Molodezhnoe otdelenie «Aktualnye problemy fundamentalnykh i prikladnykh nauk v oblasti fiziki». Otdelenie «Aktualnye problemy fundamentalnykh i prikladnykh nauk v sovremennom informatsionnom obschestve» (Moskva, MFTI, 21–26 noyabrya 2016 goda), ISBN 978-5-7417-0610-7, M.: MFTI, 2016, 1-2
2015
30.
Ryabov P. E., Savushkin A. Yu., “Fazovaya topologiya volchka Kovalevskoi–Sokolova”, Nelineinaya dinamika, 11:2 (2015), 287–317
31.
P. E. Ryabov, “New invariant relations for the generalized two-field gyrostat”, Journal of Geometry and Physics, 87, January 2015 (2015), 415–421
2017
32.
M. P. Kharlamov, P. E. Ryabov, “Topological atlas of the Kovalevskaya top in a double field”, J. Math. Sci., 223:6 (2017), 775–809
2014
33.
P. E. Ryabov, “The phase topology of a special case of Goryachev integrability in rigid body dynamics”, Sb. Math., 205:7 (2014), 1024–1044
2013
34.
P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015
2012
35.
P. E. Ryabov, M. P. Kharlamov, “Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field”, Sbornik: Mathematics, 203:2 (2012), 257–287
36.
M. P. Kharlamov, P. E. Ryabov, “Net Diagrams for the Fomenko Invariant in the Integrable System with Three Degrees of Freedom”, Doklady Mathematics, 86:3 (2012), 839–842
37.
P. E. Ryabov, G. E. Smirnov, M. P. Kharlamov, “The atlas of the diagrams for the generalization of the 4th Appelrot class of especially remarkable motions to a gyrostat in a double force field”, Mekh. Tverd. Tela, 2012, no. 42, 62-76
38.
P. E. Ryabov, “A reply to “Comments” by A. V.Tsiganov (ND, 2011, no. 3, p. 715)”, Rus. J. Nonlin. Dyn., 8:1 (2012), 167–172
2011
39.
M. P. Kharlamov, P. E. Ryabov, “Smale–Fomenko diagrams and rough topological invariants of the Kowalevski–Yehia case”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 40–59
40.
I. I. Kharlamova, P. E. Ryabov, “The electronic atlas of bifurcation diagrams of the Kowalevski–Yehia gyrostat”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2, 147–162
41.
P. E. Ryabov, “Explicit integration and the topology of the D. N. Goryachev case.”, Doklady Mathematics, 84:1 (2011), 502–505
42.
M. P. Kharlamov, P. E. Ryabov, A. Y. Savushkin, G. E. Smirnov, “Types of critical points of the Kowalevski gyrostat in double field”, Mekh. Tverd. Tela, 2011, no. 41, 27–38
2010
43.
P. E. Ryabov, “Analytic classification of singularities in the integrable Kowalevski–Yehia case”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 4, 25–30
44.
P. E. Ryabov, M. P. Kharlamov, “Analytic classification of singularities in the generalized Kowalevski case”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 2, 19–28
2007
45.
P. E. Ryabov, “Algebraic curves and bifurcation diagrams of two integrable problems (Russian)”, Mekh. Tverd. Tela, 2007, no. 37, 97–111
2003
46.
P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, Theoret. and Math. Phys., 134:2 (2003), 181–197
2001
47.
P. E. Ryabov, O. E. Orel, “Topology, bifurcations and Liouville classification of Kirchhoff equations with an additional integral of fourth degree”, Journal of Physics A: Mathematical and General, 34:11 (2001), 2149–2163
P. E. Ryabov, O. E. Orel, “Bifurcation sets in a problem on motion of a rigid body in fluid and in the generalization of this problem”, Regular and Chaotic Dynamics, 3:2 (1998), 82–91
Topology of the phase manifold and bifurcations in a generalized Lagrange top problem S. V. Sokolov, P. E. Ryabov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 12, 2023 15:00
Topological analysis of non-classical integrable problems of rigid body dynamics P. E. Ryabov International conference «Nonlinear Methods in Physics and Mechanics» dedicated to Martin Kruskal on the occasion of the 90th birthday and to the 60th anniversary of the solution of the Fermi-Pasta-Ulam problem, Yaroslavl, P. G. Demidov Yaroslavl State University, October 1–3, 2015 October 2, 2015 15:30
2023
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