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We classify five dimensional Anosov flows with smooth decomposition which are in addition transversely symplectic. Up to finite covers and a special time change, we find exectly the suspensions of symplectic hyperbolic automorphisms of four dimensional toris, and the geodesic flows of three dimensional hyperbolic manifolds.
We show that a topologically mixing $C^infty$ Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential.
We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of volume-pres
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
In this article, we give a quasi-final classification of quasiconformal Anosov flows. We deduce a very interesting differentable rigidity result for the orbit foliations of hyperbolic manifold of dimension at least three.
We prove that every sectional-Anosov flow of a compact 3-manifold $M$ exhibits a finite collection of hyperbolic attractors and singularities whose basins form a dense subset of $M$. Applications to the dynamics of sectional-Anosov flows on compact 3