Invariant tori for a class of affined Anosov mappings with quasi-periodic forces

TL;DR

This paper investigates affined Anosov mappings with quasi-periodic forces, establishing a unique integer related to the growth rate of invariant tori that matches the system's topological entropy.

Contribution

It identifies a unique integer for such systems where the exponential growth rate of invariant tori matches the topological entropy, linking geometric and dynamical complexity.

Findings

Existence of a unique integer m depending on the system

Growth rate of invariant tori of degree m equals topological entropy

Connection between invariant tori and system complexity

Abstract

In this paper, we consider a class of affined Anosov mappings with quasi-periodic forces, and show that there is a unique positive integer $m$, which only depends on the system, such that the exponential growth rate of the cardinality of invariant tori of degree $m$ is equal to the topological entropy.