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Cross sections to semi-flows on 2-complexes

Published online by Cambridge University Press:  16 January 2003

FRANÇOIS GAUTERO
FRANÇOIS GAUTERO
Affiliation:
Université de Genève, Section de Mathématiques, 2–4 rue du Lièvre, CP 240, 1211 Genève, Suisse (e-mail: [email protected])
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Abstract

A dynamical 2-complex is a 2-complex equipped with a set of combinatorial properties which allow one to define non-singular semi-flows on the complex. After giving a combinatorial characterization of the dynamical 2-complexes which define hyperbolic attractors when embedded in compact 3-manifolds, we give an effective criterion for the existence of cross sections to the semi-flows on these 2-complexes. In the embedded case, this gives an effective criterion of existence of cross sections to the associated hyperbolic attractors. We present a similar criterion for boundary-tangent flows on compact 3-manifolds which are constructed by means of our dynamical 2-complexes.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 143 - 174
Copyright
2003 Cambridge University Press

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