On the density of Birkhoff sums for Anosov diffeomorphisms
Dynamical Systems
2023-10-17 v3
Abstract
Let f be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides of zero, then the set of Birkhoff sums of all periodic points is dense in the whole set of real numbers.
Keywords
Cite
@article{arxiv.2003.03935,
title = {On the density of Birkhoff sums for Anosov diffeomorphisms},
author = {Shaobo Gan and Yi Shi and Mingyang Xia},
journal= {arXiv preprint arXiv:2003.03935},
year = {2023}
}
Comments
Final version, published in SCIENCE CHINA Mathematics