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Monodromy Representations and Lyapunov Exponents of Origamis
André Kappes
2011
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Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmüller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two.
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Keywords
- Kontsevich-Zorich cocycle
- Lyapunov exponent
- square-tiled surface
- Teichmüller curve
- variation of Hodge structures
- Veech group
Links
DOI: 10.5445/KSP/1000024418Editions