On two motions of a particle driven by equivalent ergodic and chaotic reflection laws

Abstract

In the paper we analyse dynamical systems describing the motion of a free particle in a domain on a plane (a square). We show that topologically equivalent reflection laws (each of them ergodic and chaotic) governing particle's motion at the moment of reflection can lead to two dynamical systems with entirely different qualitative properties. We also indicate a general problem of transferring such properties like chaos and ergodicity from a subsystem to the extended one.