Are generic dynamical properties stable under composition with rotations?

TL;DR

This paper investigates how the stability of measure-preserving circle maps is affected when composed with independent inner and outer rotations, focusing on their topological and measure-theoretic properties.

Contribution

It provides a detailed analysis of the stability of mixing and onto properties of Lebesgue measure-preserving circle maps under composition with independent rotations.

Findings

Stability of locally eventually onto property examined

Measure-theoretic mixing stability analyzed

Impact of independent rotations on dynamical properties

Abstract

In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving circle maps that are rotated with inner and outer rotations which are independent of each other. In particular, we analyze the stability of the locally eventually onto and measure-theoretic mixing properties.