Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Chen, Dawei¹ ; Möller, Martin²

¹ Department of Mathematics, Boston College, Carney Hall, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, USA
² Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 6-8, D-60325 Frankfurt am Main, Germany

Geometry & topology, Tome 16 (2012) no. 4, pp. 2427-2479.

Résumé

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.

Détail

DOI : 10.2140/gt.2012.16.2427

Classification : 14H10, 37D40, 14H51
Keywords: Teichmüller curve, Lyapunov exponents, Brill–Noether divisor

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