Decay of correlations on towers with non-Holder continuous Jacobian and non-exponential return time

TL;DR

This paper investigates how correlations decay in tower systems with non-Hölder Jacobians and subexponentially decaying return times, establishing subexponential bounds based on the slowest decay factors.

Contribution

It provides the first upper bounds on correlation decay rates for systems with non-Hölder Jacobians and subexponential return times.

Findings

Correlation decay is subexponential under the given conditions.

Decay rate matches the slowest of the Jacobian variation and return time decay.

Results extend understanding of statistical properties in non-uniform systems.

Abstract

We establish upper bounds on the rate of decay of correlations of tower systems with summable variation of the Jacobian and integrable return time. That is, we consider situations in which the Jacobian is not Holder and the return time is only subexponentially decaying. We obtain a subexponential bound on the correlations, which is essentially the slowest of the decays of the variation of the Jacobian and of the return time.