The Dynamics of Billiards: Between Conservative and Dissipative Regimes

Given a convex region in the plane, we can examine the associated billiard dynamics: a massless point moves along a straight line within the region and then bounces off the boundary elastically. These dynamics, introduced by G.D. Birkhoff, have been extensively studied in the literature. We will present some classical and new results, discuss other possible versions of billiard dynamics, and explore (in varying degrees of detail, depending on the time remaining) what happens when the rebound is no longer elastic but subject to dissipation.

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