On the Orbits of not Expansive Mappings in Metric Spaces

2013/04/03 by Sergio Venturini, Venturini, Sergio
Mathematics · #Advanced Topology and Set Theory #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.CV #math.DS #math.MG #msc:32F45 #msc:32H50 #msc:54E40 #msc:54E45

paper · pdf · doi:10.48550/arxiv.1304.1023

22 pages

arxiv created 2013/04/03 · arxiv updated 2013/04/04

Abstract

Let \MSpace be a locally compact metric space and let \pMap:\MSpace→\MSpace be a not expansive map. We prove that for each \ppa₀∈\MSpace the sequence \ppa₀,\pMap(\ppa₀),\pMap²(\ppa₀),… is either relatively compact in \MSpace or compactly divergent in \MSpace. As applications we study the structure of the functions which are limits of the iterates of the map \pMap and we prove the analyticity of the set of \pMap-recurrent points when \pMap:\MSpace→\MSpace is a holomorphic and \MSpace is a complex hyperbolic spaces in the sense of Kobayashi.

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