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Bounded gain of energy on the breathing circle billiard. (English) Zbl 1157.37316

Summary: The breathing circle is a two-dimensional generalization of the Fermi accelerator. It is shown that the billiard map associated to this model has invariant curves in phase space, implying that any particle will have bounded gain of energy.

MSC:

37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37E99 Low-dimensional dynamical systems
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