On boundaries of parallelizable regions of flows of free mappings. (English) Zbl 1146.37026

Summary: We are interested in the first prolongational limit set of the boundary of parallelizable regions of a given flow of the plane which has no fixed points. We prove that for every point from the boundary of a maximal parallelizable region, there exists exactly one orbit contained in this region which is a subset of the first prolongational limit set of the point. Using these uniquely determined orbits, we study the structure of maximal parallelizable regions.


37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37B99 Topological dynamics
39B12 Iteration theory, iterative and composite equations
54H20 Topological dynamics (MSC2010)
Full Text: DOI EuDML


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