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arXiv · 2009.12513

Spectral invariants of convex billiard maps:a viewpoint of Mather's beta function

Jianlu Zhang
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Abstract

For strictly convex billiard maps of smooth boundaries, we get a Birkhoff normal form via a list of constructive generating functions. Based on this, we get an explicit formula for the beta function (locally), and explored the relation between the spectral invariants of the billiard maps and the beta function.

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Jianlu Zhang. 2020-09-26. Spectral invariants of convex billiard maps:a viewpoint of Mather's beta function. https://arxiv.org/abs/2009.12513

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