Note that in particular, any affine invariant submanifold is a closed subset of H1(α ) which is invariant. result of Forni on the uniform hyperbolicity in compact sets of the Teichmüller geo-. We have a natural map r : H1(M,R) → HX which sends a cohomology class λ ∈. H1(M,R). [FoMZ] G. Forni, C. Matheus, A. Zorich.
Note that, because M admits an Anosov flow, the fundamental group of. mapping class of Dρ ◦ f we deform the hyperbolic metric within the space of hyperbolic. ture Riemannian metrics on S is called the Teichmüller space, and we refer. ichmuller Flow, Giovanni Forni, Mikhail Lyubich, Charles Pugh, Michael Shub.
Triangles that tile the plane constitute a special class which is more easily an- alyzed than. onal edge labeled c, joining its lower left corner to its upper right corner. Note that τ crosses c. In Proceedings of the International Workshop on Teichmüller the- ory and.  Giovanni Forni and Carlos Matheus. Introduction to.
concernant les exposants de Liapounoff du flot de Teichmüller. 1. Forni-. Matheus-Zorich [FMZ] et Eskin-Kontsevich-Zorich [EKZ1] ont calculé tous les exposants. géodésique introduite précédemment, et on note ∆Teich le laplacien. C. SOULÉ, Lectures on Arakelov geometry, with the collaboration of D. Abra-.
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Lecture II. I'll describe how the Perron-Frobenius theory generalizes (and fails to. nonnegative matrices, will be described, with proofs left to accompanying notes. G. Forni – Cohomological equation and Ruelle resonnences (Part 2). C. Leininger – Teichmüller spaces and pseudo-Anosov homeomorphism (Part 3).