Chaotic Dynamics in the Vertex-Splitting Rational Polygonal Billiards
In polygonal billiard dynamics, the interplay between the piece-line regular and vertex-angle singular boundary effects is related by mathematicians to the problem of integrability and by physicists to the problem of causality and randomness. We approach to the controversial issue of vertex-splitting effects by employing the alternative deterministic and stochastic schemes. The theoretical study is developed within the frameworks i) of the billiard-wall collision statistics of orbits  and ii) their survival probability, simulated in closed  and weakly open  polygons, respectively. The role of vertex-splitting effects in late-time relaxation dynamics in pseudo-integrable polygons is revealed through the comparative analyses with the ballistic dynamics in the integrable circular billiard, and the superdiffusive orbit relaxation in the chaotic Sinai billiards. In the multi-vertex polygons, the orbit-splitting events participate, due to the high-order rotational symmetry of the boundary, in the surviving of circular-like (sliding) regular orbits, be means of their modification in new irregular excitations (vortices). Having no topological analog in the geometrically corresponding circular billiard, both kinds of the orbits are observed through the universal and non-universal channels of relaxations, respectively.
Financial support by CNPq is acknowledged.