Cross-sections to semi-flows on 2-complexes

François Gautero (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

A dynamical 2-complex is a 2-complex equipped with a set of combinatorial properties which allow 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, one gives 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.

Mots clés: branched surfaces.; semi-flows; cross-section; branched surfaces

Domaines: Systèmes dynamiques [math.DS]

François Gautero. Cross-sections to semi-flows on 2-complexes. Ergodic Theory and Dynamical Systems, 2003, 23 (1), pp.143-174. ⟨hal-00807127⟩