Linearisation of conservative toral homeomorphisms and toral flows
نویسنده
چکیده
We prove an analogue of Poincaré’s classification of circle homeomorphisms for conservative homeomorphisms of the two-torus with unique rotation vector and a certain bounded mean motion property. In particular, this provides an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of conservative toral homeomorphisms. For minimal toral homeomorphisms, the result can be extended to arbitrary dimensions. Analogous results hold for toral flows.
منابع مشابه
Linearisation of conservative toral homeomorphisms
We give an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of 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 ext...
متن کاملar X iv : 0 80 3 . 24 28 v 3 [ m at h . D S ] 1 9 N ov 2 00 8 Linearization of conservative toral homeomorphisms
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 homeomor-phisms with unique rotation vector and a certain bounded mean motion property. For minimal toral homeomorphisms, the result extends to arbi...
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