Perturbative analysis of the breathing circle billiard map combined with a quantitative Mather converse-KAM criterion excludes invariant Lipschitz graphs and establishes positive topological entropy for sufficiently small angular momentum.
Mather Sets for Twist Maps and Geodesics on Tori
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Breaking of invariant curves: from the Fermi-Ulam map to the breathing circle billiard
Perturbative analysis of the breathing circle billiard map combined with a quantitative Mather converse-KAM criterion excludes invariant Lipschitz graphs and establishes positive topological entropy for sufficiently small angular momentum.