Rotor Interaction in the Annulus Billiard

Abstract

Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity.

Sub-exponential Mixing of Open Systems with Particle–Disk Interactions

“…Such systems were introduced in [18,19] and further studied in [13,20]. Even though introducing turning disks is a rather natural generalization of billiards, controlling the deterministic dynamics of such systems (event in the absence of heat reservoirs) is a delicate task and few results exist [1,7]. Consequently, the result on our paper must rely on an additional simplification: it is provided by the frequent refreshing of particles at the heat reservoirs.…”

“…The domain is assumed to be circular (see Fig. 1) as in [1], which simplifies the analysis, but is not essential and can be generalized. In addition, we introduce two vertical walls to split the domain in two.…”