`a`
Journal of Modern Dynamics (JMD)
 

Lyapunov spectrum of square-tiled cyclic covers
Pages: 319 - 353, Issue 2, April 2011

doi:10.3934/jmd.2011.5.319      Abstract        References        Full text (396.9K)           Related Articles

Alex Eskin - Department of Mathematics, University of Chicago, Chicago, IL 60637, United States (email)
Maxim Kontsevich - IHES, le Bois Marie, 35, route de Chartres, 91440 Buressur-Yvette, France (email)
Anton Zorich - IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France (email)

1 I. Bouw, "Tame Covers of Curves: P-Ranks and Fundamental Groups," Ph.D thesis, University of Utrecht, 1998.
2 I. Bouw, The $p$-rank of ramified covers of curves, Compositio Math., 126 (2001), 295-322.       
3 I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. (2), 172 (2010), 139-185.       
4 D. Chen, Covers of the projective line and the moduli space of quadratic differentials, (2010), 1-19, arXiv:1005.3120v1.
5 A. Elkin, The rank of the Cartier operator on cyclic covers of the projective line, Jour. of Algebra, 327 (2011), 1-12.       
6 A. Eskin, M. Kontsevich and A. Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, preprint.
7 G. Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. of Math. (2), 155 (2002), 1-103.       
8 G. Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle, in "Handbook of Dynamical Systems" (eds. B. Hasselblatt and A. Katok), Vol. 1B, Elsevier B.V., Amsterdam, (2006), 549-580.       
9 G. Forni, A geometric criterion for the nonuniform hyperbolicity of the Kontsevich-Zorich cocycle, J. Mod. Dyn., 5 (2011), 355-395.
10 G. Forni and C. Matheus, An example of a Teichmüller disk in genus 4 with degenerate Kontsevich-Zorich spectrum, (2008), 1-8, arXiv:0810.0023.
11 G. Forni, C. Matheus and A. Zorich, Square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 285-318.
12 S. Grushevsky and I. Krichever, The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces, in "Surveys in Differential Geometry," Vol. XIV, Geometry of Riemann Surfaces and their Moduli Spaces, Int. Press, Somerville, MA, 2009, 111-129.       
13 M. Kontsevich, Lyapunov exponents and Hodge theory, in "The Mathematical Beauty of Physics," (Saclay, 1996), Adv. Ser. Math. Phys. 24, 318-332, World Scientific Publ., River Edge, NJ, 1997.       
14 M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Inventiones Math., 153 (2003), 631-678.       
15 J. K. Koo, On holomorphic differentials of some algebraic function field of one variable over $\mathbbC$, Bull. Aust. Math. Soc., 43 (1991), 399-405.       
16 C. McMullen, Braid groups and Hodge theory, to appear in Math. Ann.
17 C. Peters, A criterion for flatness of Hodge bundles over curves and Geometric Applications, Math. Ann., 268 (1984), 1-19.       
18 G. Schmithüsen, Examples for Veech groups of origamis, in "The Geometry of Riemann Surfaces and Abelian Varieties," Contemp. Math., 397, Amer. Math. Soc., Providence, RI, (2006), 193-206.       
19 M. Schmoll, Moduli spaces of branched covers of Veech surfaces I: D-symmetric differentials, (2006), 1-40, arXiv:math.GT/0602396v1.
20 M. Schmoll, Veech groups for holonomy free torus covers, preprint, 2010.
21 J. Smillie, in preparation.
22 A. Wright, Abelian square-tiled surfaces, preprint, 2011.

Go to top