Search results for "dynamique hyperbolique"
showing 2 items of 2 documents
Dehn surgeries and smooth structures on 3-dimensional transitive Anosov flows.
2020
The present thesis is about Dehn surgeries and smooth structures associated with transitive Anosov flows in dimension three. Anosov flows constitute a very important class of dynamical systems, because of its persistent chaotic behaviour, as well as for its rich interaction with the topology of the ambient space. Even if a lot is known about the dynamical and ergodic properties of these systems, there is not a clear understanding about how to classify its different orbital equivalence classes. Until now, the biggest progress has been done in dimension three, where there is a family of techniques intended for the construction of Anosov flows called surgeries.During the realization of this th…
Dynamic instability in absence of dominated splittings.
2006
We want to understand the dynamics in absence of dominated splittings. A dominated splitting is a weak form of hyperbolicity where the tangent bundle splits into invariant subbundles, each of them is more contracted or less expanded by the dynamics than the next one. We first answer an old question from Hirsch, Pugh and Shub, and show the existence of adapted metrics for dominated splittings.Mañé found on surfaces a $C^1$-generic dichotomy between hyperbolicity and Newhouse phenomenons (infinitely many sinks/sources). For that purpose, he showed that without a strong enough dominated splitting along one periodic orbit, a $C^1$-perturbation creates a sink or a source. We generalise that last…