Periodic data rigidity of Anosov automorphisms with Jordan blocks

TL;DR

This paper studies the rigidity of Anosov automorphisms with Jordan blocks, showing that a refined periodic data can characterize conjugacy in specific cases, thus advancing understanding of their structural properties.

Contribution

It introduces a refined periodic data concept that characterizes $C^{1+}$ conjugacy for certain four-dimensional torus automorphisms with Jordan blocks.

Findings

Refined periodic data characterizes $C^{1+}$ conjugacy.

Anosov automorphisms with Jordan blocks are not periodic data rigid.

The new invariant distinguishes conjugacy classes in specific cases.

Abstract

Anosov automorphisms with Jordan blocks are not periodic data rigid. We introduce a refinement of the periodic data and show that this refined periodic data characterizes $C^{1+}$ conjugacy for Anosov automorphisms of the four dimensional torus with a Jordan block.