Title: Slow chaos in infinite settings: fluctuations and ergodicity
Abstract: Fundamental examples of slowly chaotic flows arise from billiards in (bounded) polygons and area-preserving flows on surfaces. While several classes of such flows on compact surfaces (in particular linear flows on translation surfaces and locally Hamiltonian flows) are very well understood, many questions are still widely open when the billiard or the surface are 'infinite'. Notable motivations from physics to study such flows are provided for example by the Erhenfest (windtree) model or systems of Eaton lenses. In this last talk, we will focus on some of the recent advances and open questions on two classes of such flows in infinite settings (linear flows on Abelian covers of translation surfaces and extensions of locally Hamiltonian flows). The fundamental question of 'ergodicity' turns out to be connected to a certain action on homology and to the 'fluctuations' phenomena of certain integrals along trajectories. We will conclude with an overview of recent results and open questions.
Antonio Auffinger
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