0000000001262482

AUTHOR

Andrey Gogolev

showing 2 related works from this author

Anomalous Anosov flows revisited

2017

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.

Pure mathematicsdiffeomorphismsMathematics::Dynamical Systems37D30Fiber (mathematics)General Mathematics010102 general mathematics37D30 (primary)TorusGeometric Topology (math.GT)Dynamical Systems (math.DS)Type (model theory)01 natural sciencesMathematics::Geometric TopologyPhysics::Fluid DynamicsMathematics - Geometric Topology0103 physical sciencesFOS: Mathematics010307 mathematical physicsAffine transformation0101 mathematics[MATH]Mathematics [math]Mathematics - Dynamical SystemsMathematics::Symplectic GeometryMathematics
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Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence

2020

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic flows on closed hyperbolic surfaces and for Anosov flows which admit transverse tori. We emphasize the similarity of both constructions through the concept of $h$-transversality, a tool which allows us to compose different mapping classes while retaining partial hyperbolicity. In the case of the geodesic flow of a closed hyperbolic surface $S$ we build stably ergodic, partially hyperbolic diffeomorphisms whose mapping classes form a subgroup of the mapping…

Pure mathematics37D30Similarity (geometry)Mathematics::Dynamical SystemsGeodesic[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)dynamical coherenceMSC Primary: 37C15 37D3037C1501 natural sciencessymbols.namesake0103 physical sciencesFOS: MathematicsErgodic theoryMathematics - Dynamical Systems[MATH]Mathematics [math]0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsConjecture010102 general mathematicsSurface (topology)Mathematics::Geometric Topologystable ergodicityMapping class groupFlow (mathematics)Poincaré conjecturesymbols010307 mathematical physicsGeometry and Topologypartially hyperbolic diffeomorphisms
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