Abstract
We give an equivalent condition for the existence of a semi-conjugacy to an irrational rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of Poincaré’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 toral homeomorphisms with all points non-wandering.
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Jäger, T. Linearization of conservative toral homeomorphisms. Invent. math. 176, 601–616 (2009). https://doi.org/10.1007/s00222-008-0171-5
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DOI: https://doi.org/10.1007/s00222-008-0171-5