Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-16T23:28:25.725Z Has data issue: false hasContentIssue false
  • English
  • Français

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: Francois.Gautero@math.unige.ch)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)