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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.

MSC:
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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