Linearization of conservative toral homeomorphisms

By Tobias Jäger. 2008

76 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a60245964f88fb2ec0b676582007a45d685cb17a

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In Geometry and Topology

1. Andres Koropecki
2. F. Tal

In Mathematical Physics

1. Andres Koropecki
2. F. Tal

In Statistical and Nonlinear Physics

1. Andres Koropecki
2. F. Tal

Citations in the corpus

• Strictly toral dynamics (2012, methodology): “It is also shown in [14] that every point of the set E(f )= T2 \ C(f ) belongs to some periodic topological disk U , and ρ(̂ f ,U) is a single point (however, we will not use these facts, as they are a consequence of Theorem C).”