Topological Modeling of Integrable Systems by Billiards: Realization of Numerical Invariants
V. V. Vedyushkina, В. А. Кибкало, А. Т. Фоменко
Abstract
A local version of A.T. Fomenko’s conjecture on modeling of integrable systems by billiards is formulated. It is proved that billiard systems realize arbitrary numerical marks of Fomenko–Zieschang invariants. Thus, numerical marks are not a priori a topological obstacle to the realization of the Liouville foliation of integrable systems by billiards.
Topics & Concepts
Dynamical billiardsIntegrable systemMathematicsRealization (probability)ConjectureFoliation (geology)ObstacleTopology (electrical circuits)Pure mathematicsGravitational singularityMathematical analysisGeometryCombinatoricsGeochemistryStatisticsPolitical scienceGeologyMetamorphic rockLawQuantum chaos and dynamical systemsAdvanced Differential Equations and Dynamical SystemsMathematical Dynamics and Fractals