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Structural Stability for Fibrewise Anosov Diffeomorphisms on Principal Torus Bundles

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 Added by Danyu Zhang
 Publication date 2021
  fields
and research's language is English
 Authors Danyu Zhang




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We show a fibre-preserving self-diffeomorphism which has hyperbolic splittings along the fibres on a compact principal torus bundle is topologically conjugate to a map that is linear in the fibres.



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70 - Mauricio Poletti 2017
We prove that for Anosov maps of the $3$-torus if the Lyapunov exponents of absolutely continuous measures in every direction are equal to the geometric growth of the invariant foliations then $f$ is $C^1$ conjugated to his linear part.
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We construct an example of planar Anosov diffeomorphisms without fixed points which is not topologically conjugate to a translation.
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A {em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of cite{mm}). We prove that any $C^2$ transitive sectional-Anosov flow has a unique SRB measure which is stochastically stable under small random perturbations.
In this paper we construct Cech cohomology groups that form a Gysin-type long exact sequence for principal torus bundles. This sequence is modeled on a de Rham cohomology sequence published in earlier work by Bouwknegt, Hannabuss and Mathai, which was developed to compute the global properties of T-duality in the presence of NS H-Flux.
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