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RESEARCH PRODUCT

Anomalous Anosov flows revisited

Federico Rodriguez HertzThomas BarthelméChristian BonattiAndrey Gogolev

subject

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

description

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.

yearjournalcountryeditionlanguage
2017-12-20
10.1112/plms.12321http://arxiv.org/abs/1712.07755