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Two-dimensional links and diffeomorphisms on 3-manifolds

Published online by Cambridge University Press:  19 June 2002

CHRISTIAN BONATTI ,
VIATCHESLAV GRINES  and
ELISABETH PÉCOU
CHRISTIAN BONATTI
Affiliation:
Laboratoire de Topologie, UMR 5584 du CNRS, B.P. 47 870, 21078 Dijon Cedex, France (e-mail: [email protected])
VIATCHESLAV GRINES
Affiliation:
Steklov Institute of Mathematics, Moscou State University, Vavilova str. 42, Moscou 117966, Russia (e-mail: [email protected])
ELISABETH PÉCOU
Affiliation:
Laboratoire de Topologie, UMR 5584 du CNRS, B.P. 47 870, 21078 Dijon Cedex, France (e-mail: [email protected])
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Abstract

For diffeomorphisms on 3-manifolds, two-dimensional links composed of tori (and possibly one Klein bottle) embedded in S^2\times S^1 appear in a natural way to describe the topological position of two-dimensional unstable manifolds of saddles in the basin of a periodic sink. For such a link \mathcal{E} we build a diffeomorphism f_{\mathcal{E}} which is used as a canonical model for ‘pieces of the dynamics’, namely the basin of attractors consisting of a sink and a finite set of two-dimensional unstable manifolds of saddles.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 687 - 710
Copyright
2002 Cambridge University Press

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