Geometry & Topology

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Dawei Chen and Martin Möller

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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.

Article information

Geom. Topol., Volume 16, Number 4 (2012), 2427-2479.

Received: 19 August 2011
Revised: 30 July 2012
Accepted: 31 July 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 14H51: Special divisors (gonality, Brill-Noether theory)

Teichmüller curve Lyapunov exponents Brill–Noether divisor


Chen, Dawei; Möller, Martin. Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus. Geom. Topol. 16 (2012), no. 4, 2427--2479. doi:10.2140/gt.2012.16.2427.

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