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Monodromy Representations and Lyapunov Exponents of Origamis

Kappes, André

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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DOI: 10.5445/IR/1000024435
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Hochschulschrift
Jahr 2011
Sprache Englisch
Identifikator urn:nbn:de:swb:90-244357
KITopen-ID: 1000024435
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Algebra und Geometrie (IAG)
Prüfungsdaten 25.05.2011
Referent/Betreuer Prof. G. Weitze-Schmithüsen
Schlagworte Translationsfläche, Origami, Teichmüllerkurve, Monodromiedarstellung, Variation von Hodge-Strukturen, Lyapunov-Exponent
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