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 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 -function associated to a standard-like twist map admits a unique -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}
}