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This article is cited in 24 scientific papers (total in 24 papers)
Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards
V. V. Vedyushkina, A. T. Fomenko, I. S. Kharcheva Moscow State University
Abstract:
AbstractIt is well known that surgeries of closures of solutions for integrable nondegenerate Hamiltonian systems with two degrees of freedom at a level of constant energy are classified by the so-called 3-atoms. These surgeries correspond to singular leaves of the Liouville foliation of three-dimensional isoenergetic surfaces. In this paper we prove the Fomenko conjecture that all such surgeries are modeled by integrable topological two-dimensional billiards (billiard books).
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