An analytical critical parameter is derived for the integrability-to-chaos transition in elliptical-oval billiards; increasing the elliptical component lowers the chaos threshold, while in-phase deformations can restore invariant curves.
Mathematical Proceedings of the Cambridge Philosophical Society , author=
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Critical parameters of an oval billiard with an elliptical component
An analytical critical parameter is derived for the integrability-to-chaos transition in elliptical-oval billiards; increasing the elliptical component lowers the chaos threshold, while in-phase deformations can restore invariant curves.