Limit theorems for wobbly interval intermittent maps

TL;DR

This paper establishes limit laws for a class of perturbed interval maps with indifferent fixed points, extending classical results to more complex dynamical systems with discontinuities.

Contribution

It introduces limit laws for wobbly interval intermittent maps with H"older observables, including cases with countable discontinuities, using Markov/Young towers.

Findings

Limit laws similar to semistable laws are derived.

Analysis includes maps with countable discontinuities.

Construction of Markov/Young towers is employed.

Abstract

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older observables. These limit laws are similar to the classical semistable laws previously established for random processes, but certain limitations imposed by the current dynamical set up are reflected in the main result. One of the considered examples is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.