Journal of Modern Dynamics (JMD)

Schwarz triangle mappings and Teichmüller curves: Abelian square-tiled surfaces
Pages: 405 - 426, Issue 3, July 2012

doi:10.3934/jmd.2012.6.405      Abstract        References        Full text (319.2K)           Related Articles

Alex Wright - Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637, United States (email)

1 F. Beukers, Gauss' hypergeometric functions, http://www.staff.science.uu.nl/~beuke106/MRIcourse93.ps.
2 ______, Notes on differential equations and hypergeometric functions, http://pages.uoregon.edu/njp/beukers.pdf.
3 I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. (2), 172 (2010), 139-185.       
4 J. Carlson, S. Müller-Stach and C. Peters, "Period Mappings and Period Domains," Cambridge Studies in Advanced Mathematics, 85, Cambridge University Press, Cambridge, 2003.       
5 T. A. Driscoll and L. N. Trefethen, "Schwarz-Christoffel Mapping," Cambridge Monographs on Applied and Computational Mathematics, 8, Cambridge University Press, Cambridge, 2002.       
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 ______, Lyapunov spectrum of square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 319-353.
8 G. Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. of Math. (2), 155 (2002), 1-103.       
9 ______, On the Lyapunov exponents of the Kontsevich-Zorich cocycle, in "Handbook of Dynamical Systems," Vol. 1B, Elsevier B. V., Amsterdam, (2006), 549-580.
10 G. Forni and C. Matheus, An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum, preprint, arXiv:0810.0023, 2008.
11 G. Forni, C. Matheus and A. Zorich, Square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 285-318.       
12 E. Gutkin and C. Judge, Affine mappings of translation surfaces: Geometry and arithmetic, Duke Math. J., 103 (2000), 191-213.       
13 M. Kontsevich, Lyapunov exponents and Hodge theory, in "The Mathematical Beauty of Physics" (Saclay, 1996), Adv. Ser. Math. Phys., 24, World Sci. Publ., River Edge, NJ, (1997), 318-332.       
14 H. Masur and S. Tabachnikov, Rational billiards and flat structures, in "Handbook of Dynamical Systems," Vol. 1A, North-Holland, Amsterdam, (2002), 1015-1089.       
15 C. Matheus and J.-C. Yoccoz, The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis, Journal of Modern Dynamics, 4 (2010), 453-486.       
16 M. Möller, Teichmüller curves, Galois actions and $\hat{GT}$-relations, Math. Nachr., 278 (2005), 1061-1077.       
17 ______, Shimura and Teichmüller curves, J. Mod. Dyn., 5 (2011), 1-32.
18 A. Wright, Schwarz triangle mappings and Teichmüller curves: The Veech-Ward-Bouw-Möller curves, preprint, arXiv:1203.2685, 2012.
19 M. Yoshida, "Fuchsian Differential Equations. With Special Emphasis on the Gauss-Schwarz Theory," Aspects of Mathematics, E11, Friedr. Vieweg & Sohn, Braunschweig, 1987.       
20 A. Zorich, Flat surfaces, in "Frontiers in Number Theory, Physics, and Geometry. I," Springer, Berlin, (2006), 437-583.       

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