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Complex one-frequency cocycles

Artur Avila, Svetlana Jitomirskaya, Christian Sadel (2014)

Journal of the European Mathematical Society

We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for continuous cocycles, which links non-domination with discontinuity of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are shown to depend continuously on the cocycle, even if the initial irrational frequency is allowed to vary. On the other...

Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau (2008)

Annales scientifiques de l'École Normale Supérieure

In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...

Continuum-wise expansive diffeomorphisms.

Kazuhiro Sakai (1997)

Publicacions Matemàtiques

In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.

Contracting-on-Average Baker Maps

Michał Rams (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.

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