Journal of Modern Dynamics (JMD)

Weierstrass filtration on Teichmüller curves and Lyapunov exponents

Pages: 209 - 237, Issue 2, June 2013      doi:10.3934/jmd.2013.7.209

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Fei Yu - School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China (email)
Kang Zuo - Fachbereich 08-Physik Mathematik und Informatik, Universität Mainz, 55099 Mainz, Germany (email)

Abstract: We define the Weierstrass filtration for Teichmüller curves and construct the Harder-Narasimhan filtration of the Hodge bundle of a Teichmüller curve in hyperelliptic loci and low-genus nonvarying strata. As a result we obtain the sum of Lyapunov exponents of Teichmüller curves in these strata.

Keywords:  Teichmüller curves, Lyapunov exponents, Harder-Narasimhan filtration
Mathematics Subject Classification:  Primary: 32G15; Secondary: 14H10.

Received: September 2012;      Available Online: September 2013.