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Dynamical cocycles with values in the Artin braid group

Published online by Cambridge University Press:  01 June 1999

J.-M. GAMBAUDO  and
E. E. PÉCOU
J.-M. GAMBAUDO
Affiliation:
Institut Non Linéaire de Nice, U.M.R. du C.N.R.S. 129, 1361 route des Lucioles, 06560 Valbonne, France
E. E. PÉCOU
Affiliation:
Institute for Mathematical Sciences, SUNY at Stony Brook, Stony Brook, NY 11794, USA
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Abstract

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By considering the way an $n$-tuple of points in the 2-disk are linked together under iteration of an orientation preserving diffeomorphism, we construct a dynamical cocycle with values in the Artin braid group. We study the asymptotic properties of this cocycle and derive a series of topological invariants for the diffeomorphism which enjoy rich properties.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 3 , June 1999 , pp. 627 - 641
Copyright
1999 Cambridge University Press