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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia

Dokl. RAN. Math. Inf. Proc. Upr., 2020, Volume 494, Pages 105–111 (Mi danma120)

New cases of homogeneous integrable systems with dissipation on tangent bundles of two-dimensional manifolds
M. V. Shamolin

This publication is cited in the following articles:
  1. M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. III. Sistemy sedmogo poryadka”, Materialy 6 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2024). Irkutsk, 16–20 sentyabrya 2024 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 238, VINITI, M., 2025, 69–100  mathnet  crossref
  2. M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. IV. Sistemy devyatogo poryadka”, Materialy 6 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2024). Irkutsk, 16–20 sentyabrya 2024 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 239, VINITI, M., 2025, 62–97  mathnet  crossref
  3. M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. V. Obschii sluchai”, Materialy 6 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2024). Irkutsk, 16–20 sentyabrya 2024 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 240, VINITI, M., 2025, 49–89  mathnet  crossref
  4. M. V. Shamolin, “Invariants of systems having a small number of degrees of freedom with dissipation”, Moscow University Mathematics Bulletin, 79:2 (2024), 71–84  mathnet  crossref  crossref  elib
  5. Maxim V. Shamolin, “On Integrability of Certain Classes of Variable Dissipation Systems”, PROOF, 4 (2024), 75  crossref
  6. M. V. Shamolin, “Integrability of Dynamic Equations of Generalized Four-Dimensional Pendulum Motion”, Lobachevskii J Math, 45:8 (2024), 3737  crossref
  7. M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. I. Sistemy tretego poryadka”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 236, VINITI RAN, M., 2024, 72–88  mathnet  crossref
  8. M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. II. Sistemy pyatogo poryadka”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 237, VINITI RAN, M., 2024, 49–75  mathnet  crossref
  9. M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. I. Sistemy na kasatelnykh rassloeniyakh dvumernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 100–128  mathnet  crossref
  10. M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. II. Sistemy na kasatelnykh rassloeniyakh trekhmernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 228, VINITI RAN, M., 2023, 92–118  mathnet  crossref
  11. M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. III. Sistemy na kasatelnykh rassloeniyakh chetyrekhmernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 229, VINITI RAN, M., 2023, 90–119  mathnet  crossref
  12. M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. IV. Sistemy na kasatelnykh rassloeniyakh $n$-mernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 230, VINITI RAN, M., 2023, 96–130  mathnet  crossref
  13. M. V. Shamolin, “Invariants of dynamical systems with dissipation on tangent bundles of low-dimensional manifolds”, Differential Equations, Mathematical Modeling and Computational Algorithms, Springer Proceedings in Mathematics & Statistics, 423, 2023, 167–179  crossref
  14. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 205, VINITI RAN, M., 2022, 22–54  mathnet  crossref
  15. M. V. Shamolin, “Sistemy s chetyrmya stepenyami svobody s dissipatsiei: analiz i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 205, VINITI RAN, M., 2022, 55–94  mathnet  crossref
  16. M. V. Shamolin, “Sistemy s pyatyu stepenyami svobody s dissipatsiei: analiz i integriruemost. I. Porozhdayuschaya zadacha iz dinamiki mnogomernogo tverdogo tela, pomeschennogo v nekonservativnoe pole sil”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 91–121  mathnet  crossref
  17. M. V. Shamolin, “Sistemy s pyatyu stepenyami svobody s dissipatsiei: analiz i integriruemost. II. Dinamicheskie sistemy na kasatelnykh rassloeniyakh”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 209, VINITI RAN, M., 2022, 88–107  mathnet  crossref
  18. M. V. Shamolin, “Nekotorye tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem na kasatelnom rassloenii dvumernogo mnogoobraziya”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 209, VINITI RAN, M., 2022, 108–116  mathnet  crossref
  19. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. I. Uravneniya geodezicheskikh”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 77–95  mathnet  crossref
  20. M. V. Shamolin, “Nekotorye tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 96–105  mathnet  crossref
  21. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. II. Potentsialnye silovye polya”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 29–40  mathnet  crossref
  22. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. I. Porozhdayuschaya zadacha iz dinamiki mnogomernogo tverdogo tela, pomeschennogo v nekonservativnoe pole sil”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 41–74  mathnet  crossref
  23. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. III. Silovye polya s dissipatsiei”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 120–138  mathnet  crossref
  24. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. II. Obschii klass dinamicheskikh sistem na kasatelnom rassloenii mnogomernoi sfery”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 139–148  mathnet  crossref
  25. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. III. Sistemy na kasatelnykh rassloeniyakh gladkikh $n$-mernykh mnogoobrazii”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 96–109  mathnet  crossref
  26. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. I. Uravneniya geodezicheskikh na kasatelnom rassloenii gladkogo $n$-mernogo mnogoobraziya”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 214, VINITI RAN, M., 2022, 82–106  mathnet  crossref  mathscinet
  27. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. II. Uravneniya dvizheniya na kasatelnom rassloenii k $n$-mernomu mnogoobraziyu v potentsialnom silovom pole”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 215, VINITI RAN, M., 2022, 81–94  mathnet  crossref
  28. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. III. Uravneniya dvizheniya na kasatelnom rassloenii k $n$-mernomu mnogoobraziyu v silovom pole s peremennoi dissipatsiei”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 216, VINITI RAN, M., 2022, 133–152  mathnet  crossref
  29. M. V. Shamolin, “Tensor invariants of geodesic, potential, and dissipative systems on tangent bundles of two-dimensional manifolds”, Dokl. Math., 104:3 (2021), 394–398  mathnet  crossref  crossref  zmath  elib


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