Chaotic motion in the breathing circle billiard

Abstract: We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not preserved. It is known that if the motion of the boundary is regular enough then the energy is bounded due to the existence of invariant curves. We show that it is nevertheless possible that the motion of the particle is chaotic, also under regularity assumptions for the moving boundary. More precisely, we show that there exists a class of functions describing the motion of the boundary for which the billiard map admits invariant probability measures with positive metric entropy. The proof relies on variational techniques based on Aubry-Mather theory. Joint work with Claudio Bonanno.

dynamical systems

Audience: researchers in the topic

DinAmicI: Another Internet Seminar

Series comments: For more information and for the instructions to obtain the link to the seminars, visit:

www.dinamici.org/dai-seminar/

Moreover, most seminars will be streamed live on the DinAmicI YouTube channel:

www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg