Мақаланы E-mail арқылы жіберу Level surfaces of the first integral for a billiard system with cosine refraction
- Авторлар: Nikulin M.A.1,2, Popelenskii F.Y.1,2,3
-
Мекемелер:
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- National Research University Higher School of Economics, Moscow, Russia
- Шығарылым: Том 216, № 10 (2025)
- Беттер: 101-158
- Бөлім: Articles
- URL: https://medbiosci.ru/0368-8666/article/view/331248
- DOI: https://doi.org/10.4213/sm10245
- ID: 331248
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
A new integrable system in an ellipse is introduced: the domain bounded by an ellipse is partitioned into subdomains by arcs of confocal quadrics and each subdomain is filled by a medium with fixed constant coefficient of ‘optical’ density. In crossing an interface between media the trajectory obeys the ‘cosine law’ of refraction. It is shown that such systems have an additional first integral.
For two partitions of an ellipse into subdomains the level surfaces of the additional integral are examined in detail, as well as their bifurcations arising when going over critical values of the integral.
For two partitions of an ellipse into subdomains the level surfaces of the additional integral are examined in detail, as well as their bifurcations arising when going over critical values of the integral.
Негізгі сөздер
Авторлар туралы
Mikhail Nikulin
Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia; Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: nikmihale@gmail.com
Fedor Popelenskii
Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia; Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia
Email: popelens@mech.math.msu.su
Candidate of physico-mathematical sciences, Associate professor
Әдебиет тізімі
- M. Bialy, A. E. Mironov, “The Birkhoff–Poritsky conjecture for centrally-symmetric billiard tables”, Ann. of Math. (2), 196:1 (2022), 389–413
- V. Dragovic, A. E. Mironov, “On differential equations of integrable billiard tables”, Acta Math. Sin. (Engl. Ser.), 40:1 (2024), 417–424
- A. T. Fomenko, V. V. Vedyushkina, “Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field”, Russ. J. Math. Phys., 26:3 (2019), 320–333
- M. Robnik, M. V. Berry, “Classical billiards in magnetic fields”, J. Phys. A, 18:9 (1985), 1361–1378
- M. V. Berry, M. Robnik, “Statistics of energy levels without time-reversal symmetry: {A}haronov–{B}ohm chaotic billiards”, J. Phys. A, 19:5 (1986), 649–668
- M. Bialy, A. E. Mironov, “Algebraic non-integrability of magnetic billiards”, J. Phys. A, 49:45 (2016), 455101, 18 pp.
- M. Bialy, A. E. Mironov, L. Shalom, “Magnetic billiards: non-integrability for strong magnetic field; Gutkin type examples”, J. Geom. Phys., 154 (2020), 103716, 14 pp.
- V. Dragovic, S. Gasiorek, M. Radnovic, “Billiard ordered games and books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
- M. Bialy, A. E. Mironov, S. Tabachnikov, “Wire billiards, the first steps”, Adv. Math., 368 (2020), 107154, 27 pp.
- V. Dragovic, “The Appell hypergeometric functions and classical separable mechanical systems”, J. Phys. A, 35:9 (2002), 2213–2221
Қосымша файлдар
