Аннотация:
The aim of this work is to put together two novel concepts from the theory of
integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared
recently in the work of Fomenko’s school, in particular, of V.Vedyushkina. These more complex
billiard domains are obtained by gluing planar sets bounded by arcs of confocal conics along
common edges. Such domains are used in this paper to construct the configuration space for
billiard ordered games.We analyse dynamical and topological properties of the systems obtained
in that way.
This research is partially supported by the Discovery Project No. DP200100210 Geometric
analysis of non-linear systems from the Australian Research Council, by the Mathematical Institute
of the Serbian Academy of Sciences and Arts, the Science Fund of Serbia grant Integrability and
Extremal Problems in Mechanics, Geometry and Combinatorics, MEGIC, Grant No. 7744592 and
the Ministry for Education, Science, and Technological Development of Serbia and the Simons
Foundation grant No. 854861.
Поступила в редакцию: 21.11.2021 Принята в печать: 09.02.2021
Образец цитирования:
Vladimir Dragović, Sean Gasiorek, Milena Radnović, “Billiard Ordered Games and Books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1157
https://www.mathnet.ru/rus/rcd/v27/i2/p132
Эта публикация цитируется в следующих 6 статьяx:
Г. В. Белозеров, А. Т. Фоменко, “Траекторные инварианты биллиардов и линейно интегрируемые геодезические потоки”, Матем. сб., 215:5 (2024), 3–46; G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
К. Е. Тюрина, “Топологические инварианты некоторых бильярдных упорядоченных игр”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2024, № 3, 19–25 [K. E. Turina, “Topological invariants of some ordered billiard games”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 3, 19–25]
К. Е. Тюрина, “Топологические инварианты некоторых бильярдных упорядоченных игр”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2024, № 3, 19–25; K. E. Turina, “Topological invariants of some ordered billiard games”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 79:3 (2024), 122–129
Д. А. Туниянц, “Топология изоэнергетических поверхностей бильярдных книжек, склеенных из колец”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2024, № 3, 26–35; D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Moscow University Mathematics Bulletin, 79:3 (2024), 130–141
А. Т. Фоменко, В. В. Ведюшкина, “Биллиарды и интегрируемые системы”, УМН, 78:5(473) (2023), 93–176; A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
Anatoly T. Fomenko, Vladislav A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392
Цитирование в формате AMSBIB
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