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Conjugation to a shift and the splitting of invariant manifolds

Vassiliĭ Gelfreich (1997)

Applicationes Mathematicae

We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix....

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...

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