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Loci in strata of meromorphic quadratic differentials with fully degenerate Lyapunov spectrum
1. | I2M, Université d’Aix-Marseille, 39 rue F. Joliot- Curie, 13453 Marseille Cedex 20, France, France |
References:
[1] |
D. Aulicino, Affine invariant submanifolds with completely degenerate Kontsevich-Zorich spectrum,, preprint, (2013). Google Scholar |
[2] |
I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents,, Ann. of Math. (2), 172 (2010), 139.
doi: 10.4007/annals.2010.172.139. |
[3] |
J. Chaika and A. Eskin, Every flat surface is Birkhoff and Osceledets generic in almost every direction,, preprint, (2013). Google Scholar |
[4] |
A. Eskin, M. Kontsevich and A. Zorich, Lyapunov spectrum of square-tiled cyclic covers,, J. Mod. Dyn., 5 (2011), 319.
doi: 10.3934/jmd.2011.5.319. |
[5] |
A. Eskin, M. Kontsevich and A. Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow,, Publications mathématiques de l'IHÉS, (2013), 1.
doi: 10.1007/s10240-013-0060-3. |
[6] |
A. Eskin and M. Mirzakhani, Invariant and stationary measures for the SL(2,R) action on moduli space,, preprint, (2013). Google Scholar |
[7] |
H. M. Farkas and I. Kra, Riemann Surfaces,, Second edition, (1992).
doi: 10.1007/978-1-4612-2034-3. |
[8] |
G. Forni, C. Matheus and A. Zorich, Square-tiled cyclic covers,, J. Mod. Dyn., 5 (2011), 285.
doi: 10.3934/jmd.2011.5.285. |
[9] |
G. Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus,, Ann. of Math. (2), 155 (2002), 1.
doi: 10.2307/3062150. |
[10] |
G. Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle,, in Handbook of Dynamical Systems, (2006), 549.
doi: 10.1016/S1874-575X(06)80033-0. |
[11] |
I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces,, Acta Math., 146 (1981), 231.
doi: 10.1007/BF02392465. |
[12] |
M. Möller, Shimura and Teichmüller curves,, J. Mod. Dyn., 5 (2011), 1.
doi: 10.3934/jmd.2011.5.1. |
[13] |
A. Wright, Schwarz triangle mappings and Teichmüller curves: Abelian square-tiled surfaces,, J. Mod. Dyn., 6 (2012), 405.
doi: 10.3934/jmd.2012.6.405. |
[14] |
A. Zorich, Deviation for interval-exchange transformations,, Ergodic Theory Dynam. Systems, 17 (1997), 1477.
doi: 10.1017/S0143385797086215. |
[15] |
A. Zorich, How do the leaves of a closed $1$-form wind around a surface?,, in Pseudoperiodic Topology, (1999), 135.
|
show all references
References:
[1] |
D. Aulicino, Affine invariant submanifolds with completely degenerate Kontsevich-Zorich spectrum,, preprint, (2013). Google Scholar |
[2] |
I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents,, Ann. of Math. (2), 172 (2010), 139.
doi: 10.4007/annals.2010.172.139. |
[3] |
J. Chaika and A. Eskin, Every flat surface is Birkhoff and Osceledets generic in almost every direction,, preprint, (2013). Google Scholar |
[4] |
A. Eskin, M. Kontsevich and A. Zorich, Lyapunov spectrum of square-tiled cyclic covers,, J. Mod. Dyn., 5 (2011), 319.
doi: 10.3934/jmd.2011.5.319. |
[5] |
A. Eskin, M. Kontsevich and A. Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow,, Publications mathématiques de l'IHÉS, (2013), 1.
doi: 10.1007/s10240-013-0060-3. |
[6] |
A. Eskin and M. Mirzakhani, Invariant and stationary measures for the SL(2,R) action on moduli space,, preprint, (2013). Google Scholar |
[7] |
H. M. Farkas and I. Kra, Riemann Surfaces,, Second edition, (1992).
doi: 10.1007/978-1-4612-2034-3. |
[8] |
G. Forni, C. Matheus and A. Zorich, Square-tiled cyclic covers,, J. Mod. Dyn., 5 (2011), 285.
doi: 10.3934/jmd.2011.5.285. |
[9] |
G. Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus,, Ann. of Math. (2), 155 (2002), 1.
doi: 10.2307/3062150. |
[10] |
G. Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle,, in Handbook of Dynamical Systems, (2006), 549.
doi: 10.1016/S1874-575X(06)80033-0. |
[11] |
I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces,, Acta Math., 146 (1981), 231.
doi: 10.1007/BF02392465. |
[12] |
M. Möller, Shimura and Teichmüller curves,, J. Mod. Dyn., 5 (2011), 1.
doi: 10.3934/jmd.2011.5.1. |
[13] |
A. Wright, Schwarz triangle mappings and Teichmüller curves: Abelian square-tiled surfaces,, J. Mod. Dyn., 6 (2012), 405.
doi: 10.3934/jmd.2012.6.405. |
[14] |
A. Zorich, Deviation for interval-exchange transformations,, Ergodic Theory Dynam. Systems, 17 (1997), 1477.
doi: 10.1017/S0143385797086215. |
[15] |
A. Zorich, How do the leaves of a closed $1$-form wind around a surface?,, in Pseudoperiodic Topology, (1999), 135.
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