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On chaotic dynamics in rational polygonal billiards. (English) Zbl 1128.37024
Summary: We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular motion in polygons is taken within the alternative deterministic and stochastic frameworks. The analysis is developed in terms of the billiard-wall collision distribution and the particle survival probability, simulated in closed and weakly open polygons, respectively. In the multi-vertex polygons, the late-time wall-collision events result in the circular-like regular periodic trajectories (sliding orbits), which, in the open billiard case are likely transformed into the surviving collective excitations (vortices). Having no topological analogy with the regular orbits in the geometrically corresponding circular billiard, sliding orbits and vortices are well distinguished in the weakly open polygons via the universal and non-universal relaxation dynamics.
MSC:
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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