Geometric Continued Fractions as Invariants in the Topological Classification of Anosov Diffeomorphisms of Tori

TL;DR

This paper explores how geometric continued fractions serve as invariants in classifying Anosov diffeomorphisms on tori, linking combinatorial geometry with smooth dynamical systems.

Contribution

It introduces the use of geometric continued fractions as topological invariants for classifying Anosov diffeomorphisms of tori, bridging number theory and dynamical systems.

Findings

Geometric continued fractions appear as invariants in topological classification.

A connection between combinatorial geometry and smooth dynamics is established.

New methods for classifying Anosov diffeomorphisms are proposed.

Abstract

We show how an object from the combinatorially geometric version of the analytical number theory, namely geometric continued fractions, appears in the classical smooth dynamics, namely in the problem on the topological classification of Anosov diffeomorphisms of tori.