Lyapunov spectrum of square-tiled cyclic covers

Alex Eskin, Maxim Kontsevich, Anton Zorich

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


A cyclic cover over CP1 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 Teichmüller 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.

Original languageEnglish
Pages (from-to)319-353
Number of pages35
JournalJournal of Modern Dynamics
Issue number2
Publication statusPublished - Apr 2011
Externally publishedYes


  • Cyclic cover
  • Hodge norm
  • Lyapunov exponent
  • Moduli space of quadratic differentials
  • Teichmüller geodesic flow


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