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Topology of Liouville foliations of integrable billiards on table-complexesстатья
- Авторы: Fomenko Anatoly T., Kibkalo Vladislav A.
- Журнал: European Journal of Mathematics
- Том: 8
- Номер: 4
- Год издания: 2022
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- Первая страница: 1392
- Последняя страница: 1423
- DOI: 10.1007/s40879-022-00589-7
- Аннотация: We review recent results on the class of integrable billiards and the class of integrable Hamiltonian systems. Recently introduced by Vedyushkina, classes of integrable billiards on piecewise flat manifolds or CW-complexes glued from several flat domains bounded by confocal quadrics and equipped with commuting permutations (called topological billiards or billiard books respectively), made it possible to obtain significant progress in the proof of Fomenko billiard conjecture. According to this conjecture, each topological class of Liouville foliations and non-degenerate singularities of integrable Hamiltonian systems appears in the corresponding class of integrable billiards. In other words, each non-degenerate integrable system can be realized by integrable billiards from the topological point of view. New results on the classification problem for billiard books are obtained and the general problem is reduced to classification of five finite systems of permutations with commutation conditions. Also we formulate several open problems.
- Добавил в систему: Кибкало Владислав Александрович