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Bounded recurrent sets for planar homeomorphisms

Published online by Cambridge University Press:  02 April 2001

FRÉDÉRIC LE ROUX
Affiliation:
Université Paris Sud, URA D1169 du CNRS, Bât. 425, 91405 ORSAY Cedex, France (e-mail: leroux@topo.math.u-psud.fr)

Abstract

We answer a question proposed by Barge and Franks in 1993 by showing that a bounded connected set in the plane which is closed or open and meets an infinite number of its iterates under an orientation-preserving fixed point free homeomorphism must meet all of them.

Type
Research Article
Copyright
1999 Cambridge University Press

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