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Infinite translation surfaces with infinitely generated Veech groups
1. | LATP, case cour A, Faculté des sciences Saint Jérôme, Avenue Escadrille Normandie Niemen, 13397 Marseille cedex 20, France |
2. | Institute for Algebra and Geometry, University of Karlsruhe, 76128 Karlsruhe, Germany |
References:
[1] |
J. Bowman, "Flat Structures and Complex Structures in Teichmüller Theory," Thesis (Ph.D.)–Cornell University. ProQuest LLC, Ann Arbor, MI, 2009. |
[2] |
R. G. Burns and A. M. Brunner, Two remarks on the group property of Howson, Algebra Logic, 18 (1980), 319-325.
doi: 10.1007/BF01673500. |
[3] |
R. Chamanara, Affine automorphism groups of surfaces of infinite type, In the tradition of Ahlfors and Bers, III, 123-145, Contemp. Math., 355, Amer. Math. Soc., Providence, RI, 2004. |
[4] |
E. Gutkin and C. Judge, Affine mappings of translation surfaces: Geometry and arithmetic, Duke Math. J., 103 (2000), 191-213.
doi: 10.1215/S0012-7094-00-10321-3. |
[5] |
F. Herrlich, Teichmüller curves defined by characteristic origamis, The geometry of Riemann surfaces and abelian varieties, 133-144, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006. |
[6] |
W. P. Hooper, Dynamics on an infinite surface with the lattice property, (2007) preprint, arXiv:0802.0189. |
[7] |
W. P. Hooper and B. Weiss, Generalized staircases: Recurrence and symmetry, to appear in Annales de L'Institut Fourier (2009). |
[8] |
P. Hubert and S. Lelièvre, Prime arithmetic Teichmüller discs in $H(2)$, Israel J. Math., 151 (2006), 281-321.
doi: 10.1007/BF02777365. |
[9] |
P. Hubert and S. Lelièvre, Noncongruence subgroups in $H(2)$, Int. Math. Res. Not., (2005), 47-64. |
[10] |
P. Hubert and T. Schmidt, Infinitely generated Veech groups, Duke Math. J., 123 (2004), 49-69.
doi: 10.1215/S0012-7094-04-12312-8. |
[11] |
P. Hubert and B. Weiss, Dynamics on the infinite staircase, (2008) preprint. |
[12] |
M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math., 153 (2003), 631-678.
doi: 10.1007/s00222-003-0303-x. |
[13] |
S. Lelièvre and R. Silhol, Multi-geodesic tessellations, fractional Dehn twists and uniformization of algebraic curves, (2007) preprint, arXiv:math/0702374. |
[14] |
C. McMullen, Teichmüller geodesics of infinite complexity, Acta Math., 191 (2003), 191-223.
doi: 10.1007/BF02392964. |
[15] |
P. Przytycki, G. Schmithüsen and F. Valdez, Veech groups of Loch Ness monsters,, to appear in Annales de l'Institut Fourier., ().
|
[16] |
G. Schmithüsen, "Veech Groups of Origamis," Dissertation 2005, Universität Karlsruhe. |
[17] |
G. Schmithüsen, An algorithm for finding the Veech group of an origami, Experiment. Math., 13 (2004), 459-472. |
[18] |
G. Schmithüsen, Examples for Veech groups of origamis, The geometry of Riemann surfaces and abelian varieties, 193-206, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006. |
[19] |
G. Schmithüsen, Origamis with non-congruence Veech groups, Proceedings of 34th Symposium on Transformation Groups, 31-55, Wing Co., Wakayama, 2007. |
[20] |
F. Valdez, Billiards in polygons and homogeneous foliations on $\CC^2$, Ergod. Th. & Dynam. Sys., 29 (2009), 255-271. |
[21] |
F. Valdez, Veech groups, irrational billiards and stable abelian differentials, Preprint 2009, arXiv:0905.1591v2. |
[22] |
W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math., 97 (1989), 553-583.
doi: 10.1007/BF01388890. |
show all references
References:
[1] |
J. Bowman, "Flat Structures and Complex Structures in Teichmüller Theory," Thesis (Ph.D.)–Cornell University. ProQuest LLC, Ann Arbor, MI, 2009. |
[2] |
R. G. Burns and A. M. Brunner, Two remarks on the group property of Howson, Algebra Logic, 18 (1980), 319-325.
doi: 10.1007/BF01673500. |
[3] |
R. Chamanara, Affine automorphism groups of surfaces of infinite type, In the tradition of Ahlfors and Bers, III, 123-145, Contemp. Math., 355, Amer. Math. Soc., Providence, RI, 2004. |
[4] |
E. Gutkin and C. Judge, Affine mappings of translation surfaces: Geometry and arithmetic, Duke Math. J., 103 (2000), 191-213.
doi: 10.1215/S0012-7094-00-10321-3. |
[5] |
F. Herrlich, Teichmüller curves defined by characteristic origamis, The geometry of Riemann surfaces and abelian varieties, 133-144, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006. |
[6] |
W. P. Hooper, Dynamics on an infinite surface with the lattice property, (2007) preprint, arXiv:0802.0189. |
[7] |
W. P. Hooper and B. Weiss, Generalized staircases: Recurrence and symmetry, to appear in Annales de L'Institut Fourier (2009). |
[8] |
P. Hubert and S. Lelièvre, Prime arithmetic Teichmüller discs in $H(2)$, Israel J. Math., 151 (2006), 281-321.
doi: 10.1007/BF02777365. |
[9] |
P. Hubert and S. Lelièvre, Noncongruence subgroups in $H(2)$, Int. Math. Res. Not., (2005), 47-64. |
[10] |
P. Hubert and T. Schmidt, Infinitely generated Veech groups, Duke Math. J., 123 (2004), 49-69.
doi: 10.1215/S0012-7094-04-12312-8. |
[11] |
P. Hubert and B. Weiss, Dynamics on the infinite staircase, (2008) preprint. |
[12] |
M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math., 153 (2003), 631-678.
doi: 10.1007/s00222-003-0303-x. |
[13] |
S. Lelièvre and R. Silhol, Multi-geodesic tessellations, fractional Dehn twists and uniformization of algebraic curves, (2007) preprint, arXiv:math/0702374. |
[14] |
C. McMullen, Teichmüller geodesics of infinite complexity, Acta Math., 191 (2003), 191-223.
doi: 10.1007/BF02392964. |
[15] |
P. Przytycki, G. Schmithüsen and F. Valdez, Veech groups of Loch Ness monsters,, to appear in Annales de l'Institut Fourier., ().
|
[16] |
G. Schmithüsen, "Veech Groups of Origamis," Dissertation 2005, Universität Karlsruhe. |
[17] |
G. Schmithüsen, An algorithm for finding the Veech group of an origami, Experiment. Math., 13 (2004), 459-472. |
[18] |
G. Schmithüsen, Examples for Veech groups of origamis, The geometry of Riemann surfaces and abelian varieties, 193-206, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006. |
[19] |
G. Schmithüsen, Origamis with non-congruence Veech groups, Proceedings of 34th Symposium on Transformation Groups, 31-55, Wing Co., Wakayama, 2007. |
[20] |
F. Valdez, Billiards in polygons and homogeneous foliations on $\CC^2$, Ergod. Th. & Dynam. Sys., 29 (2009), 255-271. |
[21] |
F. Valdez, Veech groups, irrational billiards and stable abelian differentials, Preprint 2009, arXiv:0905.1591v2. |
[22] |
W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math., 97 (1989), 553-583.
doi: 10.1007/BF01388890. |
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