Mathematical billiards are arguably the most visual dynamical systems which besides are considered to be relevant models for various processes in Physics. In mathematical billiards a point particle moves by inertia in some domain (billiard table) and collides elastically with the boundary of the billiard table. Some models of gases (e.g. the Boltzmann's hard spheres gas) can be reduces to mathematical billiards by introducing proper coordinates. But what will happen if in a mathematical billiard we just change a point particle by a (hard) sphere of radius r? A general opinion is that dynamics will not change and thus it is enough to consider only mathematical billiards. I will demonstrate that in fact anything can change in this case, i.e. chaotic system may become non-chaotic and vice versa. Moreover such transitions could be soft (i.e. appear for any r>0) and also "hard" (i.e. appear when r exceeds some critical value).
Participante: Dr. Leonid Bunimovich
Institución: Tecnológico de Georgia, Estados Unidos
Fecha: Miércoles, 13 de Junio de 2018