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JOURNALS // Doklady Akademii Nauk

Dokl. Akad. Nauk, 2018, Volume 479, Number 6, Pages 607–610 (Mi dan47511)

Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards
V. V. Vedyushkina, A. T. Fomenko, I. S. Kharcheva

This publication is cited in the following articles:
  1. G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  2. V. N. Zav'yalov, “Billiard with slipping by an arbitrary rational angle”, Sb. Math., 214:9 (2023), 1191–1211  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  3. A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  4. A. A. Kuznetsova, “Modeling of degenerate peculiarities of integrable billiard systems by billiard books”, Moscow University Mathematics Bulletin, 78:5 (2023), 207–215  mathnet  crossref  crossref  elib
  5. G. V. Belozerov, “Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space”, Sb. Math., 213:2 (2022), 129–160  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  6. A. T. Fomenko, V. V. Vedyushkina, “Evolutionary force billiards”, Izv. Math., 86:5 (2022), 943–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  7. V. V. Vedyushkina, V. N. Zav'yalov, “Realization of geodesic flows with a linear first integral by billiards with slipping”, Sb. Math., 213:12 (2022), 1645–1664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  8. G. V. Belozerov, “Topology of $5$-surfaces of a 3D billiard inside a triaxial ellipsoid with Hooke's potential”, Moscow University Mathematics Bulletin, 77:6 (2022), 277–289  mathnet  crossref  crossref  mathscinet  zmath  elib
  9. V. V. Vedyushkina, V. A. Kibkalo, “Billiardnye knizhki maloi slozhnosti i realizatsiya sloenii Liuvillya integriruemykh sistem”, Chebyshevskii sb., 23:1 (2022), 53–82  mathnet  crossref
  10. Anatoly T. Fomenko, Vladislav A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392  crossref
  11. V. V. Vedyushkina, I. S. Kharcheva, “Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems”, Sb. Math., 212:8 (2021), 1122–1179  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
  12. V. V. Vedyushkina, “Local modeling of Liouville foliations by billiards: implementation of edge invariants”, Moscow University Mathematics Bulletin, 76:2 (2021), 60–64  mathnet  crossref  mathscinet  zmath  isi
  13. V. A. Kibkalo, A. T. Fomenko, I. S. Kharcheva, “Realizing integrable Hamiltonian systems by means of billiard books”, Trans. Moscow Math. Soc., 82 (2021), 37–64  mathnet  crossref
  14. A. T. Fomenko, V. V. Vedyushkina, “Billiards with Changing Geometry and Their Connection with the Implementation of the Zhukovsky and Kovalevskaya Cases”, Russ. J. Math. Phys., 28:3 (2021), 317  crossref
  15. A. T. Fomenko, V. V. Vedyushkina, V. N. Zav'yalov, “Liouville Foliations of Topological Billiards with Slipping”, Russ. J. Math. Phys., 28:1 (2021), 37  crossref
  16. V. V. Vedyushkina, “Integrable billiard systems realize toric foliations on lens spaces and the 3-torus”, Sb. Math., 211:2 (2020), 201–225  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  17. I. F. Kobtsev, “An elliptic billiard in a potential force field: classification of motions, topological analysis”, Sb. Math., 211:7 (2020), 987–1013  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  18. I. S. Kharcheva, “Isoenergy manifolds of integrable billiard books”, Moscow University Mathematics Bulletin, 75:4 (2020), 149–160  mathnet  crossref  mathscinet  zmath  isi
  19. G. V. Belozerov, “Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space”, Sb. Math., 211:11 (2020), 1503–1538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  20. A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107  mathnet  crossref  mathscinet  zmath  isi
  21. V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  22. A. T. Fomenko, V. V. Vedyushkina, “Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: recent results”, Theor. Appl. Mech., 46:1 (2019), 47–63  mathnet  crossref
  23. S. E. Pustovoytov, “Topological analysis of a billiard in elliptic ring in a potential field”, J. Math. Sci., 259:5 (2021), 712–729  mathnet  crossref
  24. V. V. Vedyushkina, A. T. Fomenko, “Reducing the Degree of Integrals of Hamiltonian Systems by Using Billiards”, Dokl. Math., 99:3 (2019), 266  crossref


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