Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
Dynamical Systems
2012-11-26 v1
Abstract
We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps.
Cite
@article{arxiv.1205.1003,
title = {Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices},
author = {Michael Baake and Natascha Neumaerker and John A. G. Roberts},
journal= {arXiv preprint arXiv:1205.1003},
year = {2012}
}
Comments
29 pages, 3 figures