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arXiv · 2209.12765

Mather $\beta$-function for ellipses and rigidity

Michael Bialy
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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.

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Michael Bialy. 2022-09-26. Mather $\beta$-function for ellipses and rigidity. https://doi.org/10.3390/e24111600

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