Typical points and families of expanding interval mappings

TL;DR

This paper investigates conditions under which points are typical for a family of expanding interval maps with invariant measures, extending previous results with new assumptions.

Contribution

It provides new sufficient conditions for points to be typical in parametrized families of expanding interval maps, generalizing Schnellmann's results.

Findings

Established criteria for typicality in expanding interval maps

Extended previous results with different assumptions

Applicable to a broad class of parametrized maps

Abstract

We study parametrised families of piecewise expanding interval mappings $T_a \colon [0,1] \to [0,1]$ with absolutely continuous invariant measures $\mu_a$ and give sufficient conditions for a point $X(a)$ to be typical with respect to $(T_a, \mu_a)$ for almost all parameters $a$. This is similar to a result by D. Schnellmann, but with different assumptions.