English

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 β\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 β\beta-function to rigidity problem.

Keywords

Cite

@article{arxiv.2209.12765,
  title  = {Mather $\beta$-function for ellipses and rigidity},
  author = {Michael Bialy},
  journal= {arXiv preprint arXiv:2209.12765},
  year   = {2023}
}