Open AccessTopological obstacles to the realizability of integrable Hamiltonian systems by billiards
Author(s) -
V. V. Vedyushkina,
A. T. Fomenko
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524885471-475
Subject(s) - realizability , integrable system , degenerate energy levels , geodesic , hamiltonian system , hamiltonian (control theory) , mathematics , class (philosophy) , mathematical physics , pure mathematics , topology (electrical circuits) , physics , mathematical analysis , quantum mechanics , computer science , combinatorics , mathematical optimization , algorithm , artificial intelligence
We introduce the following classes of integrable billiards: elementary billiards, topological, books, with potential, magnetic field, geodesic billiards. These classes are used to test the A.T. Fomenko conjecture about the realizability up to Liouville equivalence by billiards of integrable non-degenerate Hamiltonian systems with two degrees of freedom. In the class of book billiards found topological obstacles to realizability.