Geometry & Topology

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Dawei Chen and Martin Möller

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732487

Digital Object Identifier
doi:10.2140/gt.2012.16.2427

Mathematical Reviews number (MathSciNet)
MR3033521

Zentralblatt MATH identifier
1266.14018

Subjects
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)

Keywords
Teichmüller curve Lyapunov exponents Brill–Noether divisor

Citation

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. https://projecteuclid.org/euclid.gt/1513732487


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