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On parallelizability of flows of free mappings. (English) Zbl 1097.39005
Summary: We consider a flow of free mappings defined on the plane. We prove that the boundary of every equivalence class of a certain equivalence relation is a union of orbits and that at most two of the boundary orbits of a class can be contained in this class. The main result says that a flow of free mappings restricted to each equivalence class of the relation is conjugate with a flow of translations. As a corollary we obtain the fact that the iterates of each arc contained in an equivalence class tend to infinity.

39B12 Iteration theory, iterative and composite equations
54H20 Topological dynamics (MSC2010)
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
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