Hitting-time Limits for some Exceptional Rare Events of Ergodic Maps

TL;DR

This paper investigates the limit distributions of hitting times for rare events in ergodic maps, providing a comprehensive analysis of their asymptotic behavior using inducing techniques.

Contribution

It introduces a novel inducing argument to analyze hitting-time limits for exceptional rare events in ergodic systems, addressing previously open questions.

Findings

Limit distributions for hitting times around periodic points are characterized.

The inducing method applies to both expanding and neutral periodic points.

The paper resolves a question from prior research [FFTV].

Abstract

We discuss limit distributions for hitting-time functions of certain exceptional families of asymptotically rare events for ergodic probability preserving transformations. The abstract core is an inducing argument. The latter applies, for example, to shrinking intervals around periodic points (both uniformly expanding and neutral) of certain finite measure preserving interval maps. In particular, we give a complete answer to a question raised in [FFTV].