English

On the regularity of Mather's $\beta$-function for standard-like twist maps

Dynamical Systems 2020-03-04 v1

Abstract

We consider the minimal average action (Mather's β\beta function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β\beta-function associated to a standard-like twist map admits a unique C1C^1-holomorphic complex extension, which coincides with this function on the set of real diophantine frequencies.

Keywords

Cite

@article{arxiv.2003.01402,
  title  = {On the regularity of Mather's $\beta$-function for standard-like twist maps},
  author = {Carlo Carminati and Stefano Marmi and David Sauzin and Alfonso Sorrentino},
  journal= {arXiv preprint arXiv:2003.01402},
  year   = {2020}
}
R2 v1 2026-06-23T14:01:44.090Z