0000000000549013

AUTHOR

Mario Shannon

showing 2 related works from this author

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…

3-ManifoldsHyperbolic DynamicsDehn surgeriesFlots d' AnosovDynamique hyperboliqueSections de BirkhoffDécompositions en livre ouvert[MATH.MATH-GN] Mathematics [math]/General Topology [math.GN]Chirurgies de DehnOpen book decompositions[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]Anosov flowsBirkhoff sections3-Variétés
researchProduct

Seifert manifolds admitting partially hyperbolic diffeomorphisms

2017

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.

Surface (mathematics)Pure mathematicsMathematics::Dynamical SystemsCircle bundle[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]0103 physical sciencesFOS: MathematicsMSC: Primary: 37D30 37C15; Secondary: 57R30 55R05.Mathematics - Dynamical Systems0101 mathematicsMathematics::Symplectic GeometrySeifert spacesMathematics - General TopologyMathematicsTransitive relationAlgebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Mathematics::Geometric TopologyFlow (mathematics)Partially hyperbolic diffeomorphisms010307 mathematical physicsDiffeomorphismAnalysis
researchProduct