Lyapunov spectrum of square-tiled cyclic covers

Alex Eskin, Maxim Kontsevich, Anton Zorich

Type: Article

Publication Date: 2011-01-01

Citations: 53

DOI: https://doi.org/10.3934/jmd.2011.5.319

Abstract

A cyclic cover over $CP^1$ branched at four points inherits a natural flatstructure from the 'pillow' flat structure on the basic sphere. We give anexplicit formula for all individual Lyapunov exponents of the Hodge bundle overthe corresponding arithmetic Teichmüller curve. The key technical element isevaluation of degrees of line subbundles of the Hodge bundle, corresponding toeigenspaces of the induced action of deck transformations.

Locations

arXiv (Cornell University) - View - PDF
MPG.PuRe (Max Planck Society) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View
DataCite API - View
Journal of Modern Dynamics - View - PDF

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