Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus
Dynamical Systems
2017-04-12 v1
Abstract
Consider the space of analytic, quasi-periodic cocycles on the higher dimensional torus. We provide examples of cocycles with nontrivial Lyapunov spectrum, whose homotopy classes do not contain any cocycles satisfying the dominated splitting property. This shows that the main result in the recent work "Complex one-frequency cocycles" by A. \'Avila, S. Jitomirskaya and C. Sadel does not hold in the higher dimensional torus setting.
Keywords
Cite
@article{arxiv.1704.03036,
title = {Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus},
author = {Pedro Duarte and Silvius Klein},
journal= {arXiv preprint arXiv:1704.03036},
year = {2017}
}
Comments
11 pages. arXiv admin note: text overlap with arXiv:1603.06851