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

Jianlu Zhang

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arxiv 2009.12513 v1 pith:5UGFPYBH submitted 2020-09-26 math.DS math.GTmath.SP

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

Jianlu Zhang This is my paper

classification math.DS math.GTmath.SP

keywords betabilliardfunctionmapsconvexinvariantsspectralbirkhoff

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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.

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

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