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An index for Brouwer homeomorphisms and homotopy Brouwer theory

Published online by Cambridge University Press:  06 October 2015

FRÉDÉRIC LE ROUX
FRÉDÉRIC LE ROUX*
Affiliation:
Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu – Paris rive gauche, 4, Place Jussieu, Case 247, Paris, 75252, France email frederic.le-roux@imj-prg.fr
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Abstract

We use the homotopy Brouwer theory of Handel to define a Poincaré index between pairs of orbits for an orientation-preserving fixed-point-free homeomorphism of the plane. Furthermore, we prove that this index is almost additive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 2 , April 2017 , pp. 572 - 605
Copyright
© Cambridge University Press, 2015 

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