Realization of bifurcations of Liouville foliations for integrable billiards in non-convex domains

TL;DR

This paper investigates the complex topological bifurcations of Liouville foliations in integrable billiard systems within non-convex domains bounded by confocal quadrics, advancing understanding of their dynamical structure.

Contribution

It provides a detailed description of 3-dimensional bifurcations of Liouville foliations in non-convex billiards, a novel analysis in this specific geometric setting.

Findings

Topology of bifurcations characterized

Liouville foliations classified in non-convex domains

New insights into integrable billiard dynamics

Abstract

A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology of 3-dimmensional bifurcations of Liouville foliations is described.