On parallelizability of flows of free mappings

• Autores: Zbigniew Lesniak
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 71, Nº. 3, 2006, págs. 280-287
• Idioma: inglés
• DOI: 10.1007/s00010-005-2808-4
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• Resumen

  • 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.