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RESEARCH PRODUCT

Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples

Kamlesh ParwaniChristian BonattiRafael Potrie

subject

Pure mathematicsFundamental groupMathematics::Dynamical SystemsGeneral Mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]MSc: 37D30[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciencesIdentity (music)Exponential growth0103 physical sciencesFOS: MathematicsMathematics - Dynamical Systems0101 mathematicsMathematicsConjecture010102 general mathematicsClassificationMathematics::Geometric TopologyDehn twistFlow (mathematics)Partially hyperbolic diffeomorphisms010307 mathematical physicsDiffeomorphism

description

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq 0$. This example contradicts a conjecture in \cite{HHU}. The main idea is to consider a well-understood time-$t$ map of a non-transitive Anosov flow and then carefully compose with a Dehn twist.

yearjournalcountryeditionlanguage
2016-12-01
https://dx.doi.org/10.48550/arxiv.1411.1221