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An origami of genus 3 with arithmetic Kontsevich–Zorich monodromy

Part of: Deformations of analytic structures Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  08 March 2019

PASCAL HUBERT  and
CARLOS MATHEUS SANTOS
PASCAL HUBERT
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, I2M - UMR 7373, 13453 Marseille, France. e-mail: hubert.pascal@gmail.com
CARLOS MATHEUS SANTOS
Affiliation:
Centre de Mathématiques Laurent Schwartz, CNRS (UMR 7640), École Polytechnique, 91128 Palaiseau, France. e-mail: carlos.matheus@math.cnrs.fr URL: http://carlos.matheus.perso.math.cnrs.fr/
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Abstract

In this we exploit the arithmeticity criterion of Oh and Benoist–Miquel to exhibit an origami in the principal stratum of the moduli space of translation surfaces of genus three whose Kontsevich–Zorich monodromy is not thin in the sense of Sarnak.

MSC classification

Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 1 , July 2020 , pp. 19 - 30
Copyright
© Cambridge Philosophical Society 2019

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