Quantitative Recurrence for Generic Homeomorphisms

TL;DR

This paper investigates the recurrence properties of generic homeomorphisms on Euclidean spaces and manifolds, revealing that their correlation decay rates are slow, which impacts understanding of their long-term statistical behavior.

Contribution

It provides new insights into the quantitative recurrence behavior of generic homeomorphisms and demonstrates the slow decay of correlations as a significant property.

Findings

Recurrence rates are quantitatively characterized.

Generic homeomorphisms exhibit slow correlation decay.

Implications for statistical properties of dynamical systems.

Abstract

In this article we study quantitative recurrence for generic home- omorphisms on euclidian spaces and compact manifolds. As an application we show that the decay of correlations of generic homeomorphisms is slow.