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Award ID contains: 1900778

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  1. ; ; (, Ergodic Theory and Dynamical Systems)
    Abstract We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles. 
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  2. ; ; (, Ergodic Theory and Dynamical Systems)
    Abstract Consider a three-dimensional partially hyperbolic diffeomorphism. It is proved that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) an Anosov diffeomorphism, a (generalized) skew-product or the time-one map of an Anosov flow, thus recovering a well-known classification conjecture of the second author to this restricted setting. 
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  3. ; (, Proceedings of the American Mathematical Society)
    We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distances) provide a source of matching functions for conjugate Anosov flows. For conservative codimension one Anosov flows φ<#comment/> t :<#comment/> M →<#comment/> M \varphi ^t\colon M\to M , dim ⁡<#comment/> M ≥<#comment/> 4 \dim M\ge 4 , these simple periodic cycle functionals are C 1 C^1 regular and, hence, can be used to improve regularity of the conjugacy. Specifically, we prove that a continuous conjugacy must, in fact, be a C 1 C^1 diffeomorphism for an open and dense set of codimension one conservative Anosov flows. 
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  4. ; (, Journal of the European Mathematical Society)
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  5. ; ; (, Journal of Modern Dynamics)
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  6. ; ; (, Annals of Mathematics)
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  7. ; ; (, Journal of the London Mathematical Society)
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  8. ; ; (, Advances in Mathematics)
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  9. ; (, Mathematische Zeitschrift)
    null (Ed.)
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  10. ; (, Discrete & Continuous Dynamical Systems - A)
    null (Ed.)
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