Cycles of links and fixed points for orientation preserving\n homeomorphisms of the open unit disk

2012/08/10 by Juliana Xavier, Xavier, Juliana
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1208.2268

openalex publication_date 2012/08/10 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28

Abstract

Michael Handel proved in Handel (1999) the existence of a fixed point for an\norientation preserving homeomorphism of the open unit disk that can be extended\nto the closed disk, provided that it has points whose orbits form an oriented\ncycle of links at infinity. More recently, the author generalized Handel's\ntheorem to a wider class of cycles of links (Xavier 2012). In this paper we\ncomplete this topic describing exactly which are all the cycles of links\nforcing the existence of a fixed point.\n

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