C1-genericity of unbounded distortion for ergodic conservative expanding circle maps

TL;DR

This paper proves that in the space of ergodic, Lebesgue-preserving C1 expanding circle maps, unbounded distortion is a generic property, meaning it occurs in a dense and typical manner.

Contribution

The paper establishes that unbounded distortion is a C1-generic property among ergodic, Lebesgue-preserving C1 expanding circle maps, advancing understanding of their typical dynamical behavior.

Findings

Unbounded distortion is C1-generic in the specified map space.

Most ergodic Lebesgue-preserving C1 expanding circle maps exhibit unbounded distortion.

The result applies to a broad class of dynamical systems on the circle.

Abstract

We prove that within the space of ergodic Lebesgue-preserving C1 expanding maps of the circle, unbounded distortion is C1-generic.