Mather $\beta$-function for ellipses and rigidity

Abstract

The goal of the first part of this note is to get an explicit formula for rotation number and Mather $\beta$-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation especially simple. In the second part we discuss application of Mather $\beta$-function to rigidity problem.

Cited by in corpus (3)

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• High-order persistence of resonant caustics in perturbed circular billiards