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Scaling features of a breathing circular billiard. (English) Zbl 1152.70014

Summary: We investigate the chaotic lowest energy region of a simplified breathing circular billiard, a two-dimensional generalization of Fermi model. When the oscillation amplitude of the breathing boundary is small and we are near the integrable to non-integrable transition, we obtain numerically that average quantities can be described by scaling functions. We also show that the map that describes this model is locally equivalent to Chirikov standard map in the region of phase space near the first invariant spanning curve.

MSC:

70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
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