-
Previous Article
Topological entropy of minimal geodesics and volume growth on surfaces
- JMD Home
- This Issue
-
Next Article
Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows
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, arXiv:1302.0913, 2013. |
[2] |
I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. (2), 172 (2010), 139-185.
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, arXiv:1305.1104, 2013. |
[4] |
A. Eskin, M. Kontsevich and A. Zorich, Lyapunov spectrum of square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 319-353.
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), 1-127.
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, arXiv:1302.3320, 2013. |
[7] |
H. M. Farkas and I. Kra, Riemann Surfaces, Second edition, Graduate Texts in Mathematics, 71, Springer-Verlag, New York, 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), 285-318.
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), 1-103.
doi: 10.2307/3062150. |
[10] |
G. Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle, in Handbook of Dynamical Systems, Vol. 1B, Elsevier B. V., Amsterdam, 2006, 549-580.
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), 231-270.
doi: 10.1007/BF02392465. |
[12] |
M. Möller, Shimura and Teichmüller curves, J. Mod. Dyn., 5 (2011), 1-32.
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), 405-426.
doi: 10.3934/jmd.2012.6.405. |
[14] |
A. Zorich, Deviation for interval-exchange transformations, Ergodic Theory Dynam. Systems, 17 (1997), 1477-1499.
doi: 10.1017/S0143385797086215. |
[15] |
A. Zorich, How do the leaves of a closed $1$-form wind around a surface?, in Pseudoperiodic Topology, Amer. Math. Soc. Transl. Ser. 2, 197, Amer. Math. Soc., Providence, RI, 1999, 135-178. |
show all references
References:
[1] |
D. Aulicino, Affine invariant submanifolds with completely degenerate Kontsevich-Zorich spectrum, preprint, arXiv:1302.0913, 2013. |
[2] |
I. I. Bouw and M. Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. (2), 172 (2010), 139-185.
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, arXiv:1305.1104, 2013. |
[4] |
A. Eskin, M. Kontsevich and A. Zorich, Lyapunov spectrum of square-tiled cyclic covers, J. Mod. Dyn., 5 (2011), 319-353.
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), 1-127.
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, arXiv:1302.3320, 2013. |
[7] |
H. M. Farkas and I. Kra, Riemann Surfaces, Second edition, Graduate Texts in Mathematics, 71, Springer-Verlag, New York, 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), 285-318.
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), 1-103.
doi: 10.2307/3062150. |
[10] |
G. Forni, On the Lyapunov exponents of the Kontsevich-Zorich cocycle, in Handbook of Dynamical Systems, Vol. 1B, Elsevier B. V., Amsterdam, 2006, 549-580.
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), 231-270.
doi: 10.1007/BF02392465. |
[12] |
M. Möller, Shimura and Teichmüller curves, J. Mod. Dyn., 5 (2011), 1-32.
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), 405-426.
doi: 10.3934/jmd.2012.6.405. |
[14] |
A. Zorich, Deviation for interval-exchange transformations, Ergodic Theory Dynam. Systems, 17 (1997), 1477-1499.
doi: 10.1017/S0143385797086215. |
[15] |
A. Zorich, How do the leaves of a closed $1$-form wind around a surface?, in Pseudoperiodic Topology, Amer. Math. Soc. Transl. Ser. 2, 197, Amer. Math. Soc., Providence, RI, 1999, 135-178. |
[1] |
Corentin Boissy. Classification of Rauzy classes in the moduli space of Abelian and quadratic differentials. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3433-3457. doi: 10.3934/dcds.2012.32.3433 |
[2] |
Jonathan Chaika, Yitwah Cheung, Howard Masur. Winning games for bounded geodesics in moduli spaces of quadratic differentials. Journal of Modern Dynamics, 2013, 7 (3) : 395-427. doi: 10.3934/jmd.2013.7.395 |
[3] |
Anton Zorich. Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials. Journal of Modern Dynamics, 2008, 2 (1) : 139-185. doi: 10.3934/jmd.2008.2.139 |
[4] |
Jonathan DeWitt. Local Lyapunov spectrum rigidity of nilmanifold automorphisms. Journal of Modern Dynamics, 2021, 17: 65-109. doi: 10.3934/jmd.2021003 |
[5] |
Keith Burns, Katrin Gelfert. Lyapunov spectrum for geodesic flows of rank 1 surfaces. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1841-1872. doi: 10.3934/dcds.2014.34.1841 |
[6] |
Alex Eskin, Maxim Kontsevich, Anton Zorich. Lyapunov spectrum of square-tiled cyclic covers. Journal of Modern Dynamics, 2011, 5 (2) : 319-353. doi: 10.3934/jmd.2011.5.319 |
[7] |
Luis Barreira, Claudia Valls. Quadratic Lyapunov sequences and arbitrary growth rates. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 63-74. doi: 10.3934/dcds.2010.26.63 |
[8] |
Jian-Hua Zheng. Dynamics of hyperbolic meromorphic functions. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2273-2298. doi: 10.3934/dcds.2015.35.2273 |
[9] |
Freddy Dumortier, Christiane Rousseau. Study of the cyclicity of some degenerate graphics inside quadratic systems. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1133-1157. doi: 10.3934/cpaa.2009.8.1133 |
[10] |
Gisella Croce. An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 507-530. doi: 10.3934/dcdss.2012.5.507 |
[11] |
Jordi-Lluís Figueras, Thomas Ohlson Timoudas. Sharp $ \frac12 $-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4519-4531. doi: 10.3934/dcds.2020189 |
[12] |
Zuxing Xuan. On conformal measures of parabolic meromorphic functions. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 249-257. doi: 10.3934/dcdsb.2015.20.249 |
[13] |
Dawei Chen. Strata of abelian differentials and the Teichmüller dynamics. Journal of Modern Dynamics, 2013, 7 (1) : 135-152. doi: 10.3934/jmd.2013.7.135 |
[14] |
Ferrán Valdez. Veech groups, irrational billiards and stable abelian differentials. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 1055-1063. doi: 10.3934/dcds.2012.32.1055 |
[15] |
Agnieszka Badeńska. Measure rigidity for some transcendental meromorphic functions. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2375-2402. doi: 10.3934/dcds.2012.32.2375 |
[16] |
C. T. Cremins, G. Infante. A semilinear $A$-spectrum. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 235-242. doi: 10.3934/dcdss.2008.1.235 |
[17] |
Thomas Kappeler, Yannick Widmer. On nomalized differentials on spectral curves associated with the sinh-Gordon equation. Journal of Geometric Mechanics, 2021, 13 (1) : 73-143. doi: 10.3934/jgm.2020023 |
[18] |
Juan J. Morales-Ruiz, Sergi Simon. On the meromorphic non-integrability of some $N$-body problems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1225-1273. doi: 10.3934/dcds.2009.24.1225 |
[19] |
Shahar Nevo, Xuecheng Pang and Lawrence Zalcman. Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros. Electronic Research Announcements, 2006, 12: 37-43. |
[20] |
Jaume Llibre, Yuzhou Tian. Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4. Discrete and Continuous Dynamical Systems - B, 2022, 27 (8) : 4305-4316. doi: 10.3934/dcdsb.2021228 |
2021 Impact Factor: 0.641
Tools
Metrics
Other articles
by authors
[Back to Top]