Équations cohomologiques de flots riemanniens et de difféomorphismes d’Anosov

Abstract

In this paper: i) We compute the leafwise cohomology of a complete Riemannian Diophantine flow. ii) We solve explicitly the discrete cohomological equation for the Anosov diffeomorphism on the torus Tⁿ defined by a hyperbolic and diagonalizable matrix A∈SL(n,Z) whose eigenvalues are all real positive numbers. We use this to solve the continuous cohomological equation of the Anosov flow \\mathcal{F} on the hyperbolic torus T_Aⁿ⁺¹ obtained from A by suspension. This enables us to compute some other geometrical objects associated to the diffeomorphism A and the foliation \\mathcal{F} like the invariant distributions and the leafwise cohomology.