Resonances for rational Anosov maps on the torus
Abstract
A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps with the sequence of resonances decaying stretched-exponentially. This is achieved by introducing a certain group of rational toral diffeomorphisms and computing the resonances of the respective composition operator considered on suitable anisotropic spaces of hyperfunctions. The class of examples is sufficiently rich to also include non-linear Anosov maps with trivial resonances, or resonances decaying exponentially, as well as with or without area-preservation or reversing symmetries.
Keywords
Cite
@article{arxiv.2211.05925,
title = {Resonances for rational Anosov maps on the torus},
author = {Julia Slipantschuk and Oscar F. Bandtlow and Wolfram Just},
journal= {arXiv preprint arXiv:2211.05925},
year = {2022}
}
Comments
46 pages, 4 figures