About Imperfect Mushroom Billiards

TL;DR

This paper investigates how small imperfections in mushroom billiards, such as corner rounding and angle deviations, influence their dynamical behavior, revealing transitions between regular and chaotic regimes with unexpected features.

Contribution

It provides a detailed analysis of the effects of imperfections on mushroom billiards, highlighting non-generic features and transition scenarios not previously characterized.

Findings

Imperfections cause transitions from mushroom to KAM or chaotic behavior.

Rounded corners lead to fractal islands and chaos.

Small deviations significantly alter the billiard dynamics.

Abstract

Imperfections of Bunimovich mushroom Billiards are analyzed. Any experiment will be affected by such imperfections, and it will be necessary to estimate their influence. In particular some of the corners will be rounded and small deviations of the angle of the underside of the mushroom head will be considered. The analysis displayed some unexpected non-generic features. The latter leads to a transition from a perfect mushroom behavior to either an ordinary KAM scenario or an abrupt transition to complete chaos, depending on the sign of the perturbation. The former produces a fractal area of islands and chaos, in fact a KAM scenario, not associated to the large island of stability of the mushroom billiard.