Anosov automorphisms on nilmanifolds in dimensions 9 and 10

Abstract

We study 9 and 10-dimensional Anosov Lie algebras, by using the properties of very special algebraic numbers. We classify k-step complex Anosov Lie algebras for $k>2$ and in the two step case, we give an example in each possible type, or we give a non-existence result.

A new paper "Characterization of of 9-dimensional Anosov Lie algebras", arXiv:1411.2006, was submitted which contains stronger results than this version. Work on 10-dimensional Anosov Lie algebras is in progress