Slow entropy for some Anosov-Katok diffeomorphisms

TL;DR

This paper develops methods to compute slow entropy, a complexity measure for entropy-zero systems, specifically applied to Anosov-Katok diffeomorphisms, enhancing understanding of their dynamical properties.

Contribution

It introduces new mechanisms for calculating topological and measure-theoretic slow entropy of Anosov-Katok diffeomorphisms, advancing the analysis of their complexity.

Findings

Methods for computing slow entropy of Anosov-Katok diffeomorphisms

Enhanced understanding of complexity in entropy-zero systems

Tools for analyzing ergodic and topological properties

Abstract

The Anosov-Katok method is one of the most powerful tools of constructing smooth volume-preserving diffeomorphisms of entropy zero with prescribed ergodic or topological properties. To measure the complexity of systems with entropy zero, invariants like slow entropy have been introduced. In this article we develop several mechanisms facilitating computation of topological and measure-theoretic slow entropy of Anosov-Katok diffeomorphisms.