Séminaire Teich : 11 h 00
Mario Shannon speak about the flots d’Anosov.
The subject : Open book decompositions of a suspension Anosov flow and affine structures.
Despite the good comprehension that we have nowadays about the asymp- totic dynamical behaviour of a general Anosov flow, classification of the different orbital equivalent classes rest a major subject nowadays. In the particular case of dimension three, a lot of different examples of Anosov flows can be constructed using surgery methods, which shows that the set of different equivalence classes is not at all simple to describe.
If we restrict to the special subfamily of transitive 3-dimensional Anosov flows, each flow has (many) associated open book decompositions of the 3- manifold with pseudo-Anosov monodromy. Since pseudo-Anosov homeomor- phisms can be classified by terms of a combinatorial invariant, there is a hope to produce combinatorial invariants of the orbital equivalence class of these Anosov flows in terms of those available for pseudo-Anosov. The problem to solve is : Given two open book decompositions with pseudo-Anosov monodromy, how to determine if both correspond to the same flow?
We study a simpler question related to the previous one: Given an open book decomposition with pseudo-Anosov monodromy, can we determine whether or not the corresponding Anosov flow is a suspension Anosov flow ? In this talk we will provide a criterion for this question based on the existence of some affine incomplete structures associated with the pseudo-Anosov monodromy. In turn, we can provide a natural bijection between the set of genus one Birkhoff sections of a suspension Anosov flow and these affine structures.
Friday at 11am
Location: FRUMAM premises (Saint Charles campus)
The Teich is a weekly working group, which has historically developed around the Teichmuller spaces.
They include dynamic systems, geometry, group geometry, ergodic theory, combinatorics, etc.
Organizers: Thierry Coulbois – olga Romaskevich
More information here: https://www.i2m.univ-amu.fr/agenda/seminaires/teich/
Séminaire Teich : 11 h
Mario Shannon Will speak of the iModèles hyperboliques des flots topologiques d’Anosov transtitifs.
Hyperbolic models of transitive topological Anosov flows.
A topological Anosov flow on a closed 3-manifold is a non-singular flow that resembles very much a smooth Anosov flow: It is expansive and satisfies the (global) shadowing property. Moreover, it preserves a pair of transverse sta- ble/unstable foliations that intersect along the orbits of the flow. The main difference with a (smooth) Anosov flow is the lack of a global uniformly hyper- bolic structure.
We investigate the question of weather or not every topological Anosov flow in a 3-manifold is, actually, orbit equivalent with some smooth Anosov flow. Apart from its own theoretical interest, this question appears related with some techniques for the construction of Anosov flows on 3-manifolds, notably with the so called Fried surgery.
Our work consists in show that, under the hypothesis of transitivity, every topological Anosov flow is orbitally equivalent with a smooth Anosov flow.
In this talk we are going to present the main ideas and difficulties behind the construction of these smooth hyperbolic models associated with transitive topological Anosov flows. As well, we will give a flavour of how this study can be reduced to pseudo-Anosov dynamics on surfaces with boundary.