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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Dawei Chen and Martin Möller

Geometry & Topology 16 (2012) 2427–2479
Abstract

We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.

Keywords
Teichmüller curve, Lyapunov exponents, Brill–Noether divisor
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 37D40, 14H51
References
Publication
Received: 19 August 2011
Revised: 30 July 2012
Accepted: 31 July 2012
Published: 5 February 2013
Proposed: Benson Farb
Seconded: Shigeyuki Morita, Walter Neumann
Authors
Dawei Chen
Department of Mathematics
Boston College
Carney Hall
140 Commonwealth Avenue
Chestnut Hill
MA 02467
USA
Martin Möller
Institut für Mathematik
Goethe-Universität Frankfurt
Robert-Mayer-Str. 6-8
D-60325 Frankfurt am Main
Germany