Explicit Correlation Bounds for Expanding Circle Maps Using the Coupling Method
Dynamical Systems
2013-03-12 v2 Mathematical Physics
math.MP
Probability
Abstract
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical, the coupling method is relatively modern and employed here for the first time to yield explicit bounds in terms of system constants. The work constitutes a part of the author's Bachelor's thesis. The author hopes that the manuscript can serve as a useful introduction to the flexible coupling method in the theory of dynamical systems.
Cite
@article{arxiv.1211.2438,
title = {Explicit Correlation Bounds for Expanding Circle Maps Using the Coupling Method},
author = {Henri Sulku},
journal= {arXiv preprint arXiv:1211.2438},
year = {2013}
}
Comments
17 pages. A harmless error in the proof of Theorem 3.2. and some typos corrected in this version: few numerical values slightly improved