A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point

TL;DR

This paper provides a straightforward proof demonstrating the exactness of a broad class of intermittent expanding maps on the interval, characterized by neutral fixed points and multiple branches, relevant in nonlinear dynamics and ergodic theory.

Contribution

It introduces a simple proof confirming the exactness of certain expanding maps with indifferent fixed points, expanding understanding in dynamical systems theory.

Findings

Proves exactness for a wide class of intermittent maps

Includes maps with countably many branches and neutral fixed points

Simplifies previous proofs in the field

Abstract

Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with countably many surjective branches and a strongly neutral fixed point in 0.