Linearisation of conservative toral homeomorphisms

Details Linearisation of conservative toral homeomorphisms Linearisation of conservative toral homeomorphisms

2008-03-17

arxiv.org/abs/0803.2428v3

Mathematics

Dynamical Systems

11 pages; final version, to appear in Inventiones mathematicae. An erroneous remark concerning a result of Misiurewicz and Zie

Scientific paper

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.

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