Linearisation of conservative toral homeomorphisms
Dynamical Systems
2015-05-13 v3
Abstract
We give an equivalent characterisation for the existence of a semi-conjugacy to an irrational rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of Poincare's classification of circle homeomorphisms for conservative toral homeomorphisms with unique rotation vector and a certain bounded mean motion property. For minimal toral homeomorphisms, the result extends to arbitrary dimensions. Further, we provide a basic classification for the dynamics of non-wandering toral homeomorphisms homotopic to the identitiy.
Cite
@article{arxiv.0803.2428,
title = {Linearisation of conservative toral homeomorphisms},
author = {T. Jaeger},
journal= {arXiv preprint arXiv:0803.2428},
year = {2015}
}
Comments
11 pages; final version, to appear in Inventiones mathematicae. An erroneous remark concerning a result of Misiurewicz and Ziemian was deleted