Symplectic Partially Hyperbolic Automorphisms of 6-Torus

TL;DR

This paper classifies symplectic partially hyperbolic automorphisms of a 6-torus, focusing on the (2,2,2) eigenvalue configuration, and analyzes their topological properties and decomposability.

Contribution

It provides a classification of such automorphisms in the (2,2,2) case, including transitive and decomposable scenarios, expanding understanding of their topological structure.

Findings

Classification of automorphisms in the (2,2,2) case

Analysis of transitive and decomposable cases

Topological properties of these automorphisms

Abstract

We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic structure given by an integer skew-symmetric non-degenerate matrix. Such a symplectic matrix generates a partially hyperbolic automorphism of the torus, if it has eigenvalues both outside and on the unit circle. We study the case (2,2,2), numbers are dimensions of stable, center and unstable subspaces of the matrix. We study transitive and decomposable cases possible here and present a classification in both cases.