Mather $\beta$-function for ellipses and rigidity
Dynamical Systems
2023-08-03 v2 Differential Geometry
Abstract
The goal of the first part of this note is to get an explicit formula for rotation number and Mather -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 -function to rigidity problem.
Cite
@article{arxiv.2209.12765,
title = {Mather $\beta$-function for ellipses and rigidity},
author = {Michael Bialy},
journal= {arXiv preprint arXiv:2209.12765},
year = {2023}
}