Anton Zorich
Lyapunov spectrum of square-tiled cyclic covers.
Mon, 08/02/2010 - 15:01 — SomNambulAuthors: Anton Zorich, Alex Eskin, Maxim Kontsevich
Subjects: Dynamical Systems
AbstractA cyclic cover over the Riemann sphere branched at four points inherits a
natural flat structure from the "pillow" flat structure on the basic sphere. We
give an explicit formula for all individual Lyapunov exponents of the Hodge
bundle over the corresponding arithmetic Teichmuller curve. The key technical
element is evaluation of degrees of line subbundles of the Hodge bundle,
corresponding to eigenspaces of the induced action of deck transformations.Square-tiled cyclic covers.
Tue, 07/27/2010 - 15:01 — SomNambulAuthors: Carlos Matheus, Giovanni Forni, Anton Zorich
Subjects: Dynamical Systems
AbstractA cyclic cover of the projective plane branched at four points has a natural
structure of a square-tiled surface. We describe the combinatorics of such a
square-tiled surface, the geometry of the corresponding Teichm\"uller curve,
and compute the Lyapunov exponents of the determinant bundle over the
Teichm\"uller curve with respect to the geodesic flow.
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