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Topology and its Applications 153 (2006) 11921201 www.elsevier.com/locate/topol
 

Summary: Topology and its Applications 153 (2006) 11921201
www.elsevier.com/locate/topol
Pointwise recurrent homeomorphisms with stable
fixed points
Konstantin Athanassopoulos
Department of Mathematics, University of Crete, GR-71409 Iraklion, Greece
Received 26 September 2003; accepted 13 January 2005
Abstract
We prove that a pointwise recurrent, orientation preserving homeomorphism of the 2-sphere,
which is different from the identity and whose fixed points are stable in the sense of Lyapunov
must have exactly two fixed points. If moreover there are no periodic points, other than fixed, then
every stable minimal set is connected and its complement has exactly two connected components.
Finally, we study liftings of the restriction to the complement of the fixed point set to the universal
covering space.
2005 Elsevier B.V. All rights reserved.
MSC: 54H20; 37B20
Keywords: Pointwise recurrent homeomorphism; Stable fixed point; 2-sphere
1. Introduction
A homeomorphism f :X X of a compact metrizable space X is called pointwise
recurrent if x L+(x) L-(x) for every x X, where

  

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

 

Collections: Mathematics