November 8, 2025Open Access

Non-Birkhoff periodic orbits in symmetric billiards

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Analysis shows non-Birkhoff periodic orbits with prescribed rotation numbers in symmetric billiards, indicating complex dynamics may arise.

Non-Birkhoff periodic orbits are shown to exist in symmetric convex planar billiards, with various rotation numbers.
A quantitative criterion enables the identification of conditions for the existence of such orbits.
Analysis includes generalization to D_2-symmetric billiards from established results in elliptical billiards.
These findings support the idea that small perturbations can lead to diverse orbit behaviors.

Oelen et al. (2025) studied this question.

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Analysis shows non-Birkhoff periodic orbits with prescribed rotation numbers in symmetric billiards, indicating complex dynamics may arise.