Open AccessThe reduction of the degree of integrals of hamiltonian systems with the help of billiards
Author(s) -
V. V. Vedyushkina,
Виктория Викторовна Ведюшкина,
А. Т. Фоменко,
А. Т. Фоменко
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524862151-155
Subject(s) - integrable system , bounded function , hamiltonian system , quadratic equation , mathematics , hamiltonian (control theory) , degree (music) , pure mathematics , mathematical physics , mathematical analysis , physics , geometry , mathematical optimization , acoustics
In the theory of integrable Hamiltonian systems with two degrees of freedom there are widely known integrable systems whose integrals have a high degree, namely 3 and 4: the Kovalevskaya system and its generalizations - the Kovalevskaya - Yahya system and the Kovalevskaya system on the Lie algebra so(4), Goryachev-Chaplygin-Sretensky, Sokolov and Dullin-Matveyev. The article shows that using integrable billiards bounded by arcs of confocal quadrics decreases the degree of integrals 3 and 4 of these systems fo some isoenergy 3-surfaces. Moreover, the integrals of degree 3 and 4 reduce to the same canonical quadratic integral on billiards.