Geodesic
Topological modeling of integrable systems by billiards: realization of numerical invariants
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 9-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A local version of A.T. Fomenko's conjecture on modeling of integrable systems by billiards is formulated. It is proved that billiard systems realize arbitrary numerical marks of Fomenko–Zieschang invariants. Thus, numerical marks are not a priori a topological obstacle to the realization of the Liouville foliation of integrable systems by billiards.
Keywords: integrability, Hamiltonian system, CW complex.
Mots-clés : billiard, Fomenko–Zieschang invariant 
@article{DANMA_2020_493_a1,
     author = {V. V. Vedyushkina and V. A. Kibkalo and A. T. Fomenko},
     title = {Topological modeling of integrable systems by billiards: realization of numerical invariants},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {9--12},
     year = {2020},
     volume = {493},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_493_a1/}
}
TY  - JOUR
AU  - V. V. Vedyushkina
AU  - V. A. Kibkalo
AU  - A. T. Fomenko
TI  - Topological modeling of integrable systems by billiards: realization of numerical invariants
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 9
EP  - 12
VL  - 493
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_493_a1/
LA  - ru
ID  - DANMA_2020_493_a1
ER  - 
%0 Journal Article
%A V. V. Vedyushkina
%A V. A. Kibkalo
%A A. T. Fomenko
%T Topological modeling of integrable systems by billiards: realization of numerical invariants
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 9-12
%V 493
%U http://geodesic.mathdoc.fr/item/DANMA_2020_493_a1/
%G ru
%F DANMA_2020_493_a1
V. V. Vedyushkina; V. A. Kibkalo; A. T. Fomenko. Topological modeling of integrable systems by billiards: realization of numerical invariants. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 9-12. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a1/

[1] Glutsyuk A.A., DAN, 481:6 (2018), 594–598 | Zbl

[2] Bolotin S.V., Vestn. Mosk. un-ta. Matem. Mekhan., 1990, no. 2, 33–36

[3] Bialy M., Mironov A.E., Adv. Math., 313 (2017), 102–126 | DOI | MR | Zbl

[4] Bialy M., Mironov A.E., J. Geom. Phys., 115 (2017), 150–156 | DOI | MR | Zbl

[5] Avila A., Simoi J.De, Kaloshin V., Ann. of Math., 184:2 (2016), 527–558 | DOI | MR | Zbl

[6] Kaloshin V., Sorrentino A., Ann. of Math., 188:1 (2018), 315–380 | DOI | MR | Zbl

[7] Bialy M., Mironov A.E., J. Phys. A, 49:45 (2016), 455101, 18 pp. | DOI | MR | Zbl

[8] Byalyi M., Mironov A.E., UMN, 74:2 (446) (2019), 3–26 | DOI | MR

[9] Vedyushkina V.V., Kharcheva I.S., Matem. sb., 209:12 (2018), 17–56 | DOI | MR | Zbl

[10] Bolsinov A.V., Fomenko A.T., Integriruemye gamiltonovy sistemy. Geometriya, topologiya, klassifikatsiya, v. 1, Izd. dom “Udmurtskii universitet”, Izhevsk, 1999, 444 pp.

[11] Vedyushkina V.V., Fomenko A.T., Izv. RAN. Seriya matem., 83:6 (2019), 63–103 | DOI | MR | Zbl

[12] Vedyushkina V.V., Fomenko A.T., Vestn. Mosk. un-ta. Matem. Mekhan., 2019, no. 3, 15–25 | MR | Zbl

[13] Pustovoitov S.E., Fund. prikl. mat., 22:6 (2019), 201–225 | MR

[14] Fomenko A.T., Vedyushkina V.V., Russ. J. Math. Phys., 26:3 (2019), 320–333 | DOI | MR | Zbl

[15] Karginova E.E., Matem. sb., 211:1 (2020), 3–31 | DOI | MR | Zbl