Topologically Anosov plane homeomorphisms.

This paper deals with classifying the dynamics of topologically Anosov plane homeomorphisms. We prove that a topologically Anosov homeomorphism f : R 2 → R 2 is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwandering set of f reduces to a fixed point, or if there exists an open, connected, simply connected proper subset U such that f(U) ⊂ Int(U), and such that ∪ n≤0 f n (U) = R 2 . In the general case, we prove a structure theorem for the α-limits of orbits with empty ω-limit (or the ω-limits of orbits with empty α-limit).