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Real bounds and Lyapunov exponents
A combinatorial proof of the Kontsevich-Zorich-Boissy classification of Rauzy classes
1. | Fine Hall - Washington Road, Princeton, NJ 08544-1000, United States |
References:
[1] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture,, Acta Math., 198 (2007), 1.
doi: 10.1007/s11511-007-0012-1. |
[2] |
C. Boissy, Classification of Rauzy classes in the moduli space of quadratic differentials,, Discrete and Continuous Dynam. Systems - A, 32 (2012), 3433.
doi: 10.3934/dcds.2012.32.3433. |
[3] |
C. Boissy, Labeled rauzy classes and framed translation surfaces,, Annales de L'Institut Fourier, 63 (2013), 547.
doi: 10.5802/aif.2769. |
[4] |
C. Boissy, A combinatorial move on the set of jenkins-strebel differentials,, preprint, (). Google Scholar |
[5] |
C. Boissy and E. Lanneau, Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials,, Ergodic Theory Dynam. Systems, 29 (2009), 767.
doi: 10.1017/S0143385708080565. |
[6] |
D. Chen and M. Möller, Quadratic differentials in low genus: Exceptional and non-varying,, Annales scientifiques de l'École normale supérieure, 47 (2014), 309.
|
[7] |
V. Delecroix, Cardinality of Rauzy classes,, Annales de l'institute Fourier, 63 (2013), 1651.
doi: 10.5802/aif.2811. |
[8] |
J. Fickenscher, Self-inverses in Rauzy Classes,, Ph.D thesis, (2011).
|
[9] |
J. Fickenscher, Labeled and non-labeled extended Rauzy classes,, preprint, (). Google Scholar |
[10] |
J. Fickenscher, Self-inverses, Lagrangian permutations and minimal interval exchange transformations with many ergodic measures,, Comm. in Contemporary Mathematics, 16 (2014).
doi: 10.1142/s0219199713500193. |
[11] |
M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities,, Invent. Math., 153 (2003), 631.
doi: 10.1007/s00222-003-0303-x. |
[12] |
E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials,, Annales scientifiques de l'École normale supérieure, 41 (2008), 1.
|
[13] |
G. Rauzy, Échanges d'intervalles et transformations induites,, Acta Arith., 34 (1979), 315.
|
[14] |
W. A. Veech, Gauss measures for transformations on the space of interval exchange maps,, Ann. of Math. (2), 115 (1982), 201.
doi: 10.2307/1971391. |
[15] |
W. A. Veech, Moduli spaces of quadratic differentials,, J. Analyse Math., 55 (1990), 117.
doi: 10.1007/BF02789200. |
[16] |
M. Viana, Ergodic theory of interval exchange maps,, Rev. Mat. Complut., 19 (2006), 7.
doi: 10.5209/rev_rema.2006.v19.n1.16621. |
[17] |
A. Zorich, Explicit Jenkins-Strebel representatives of all strata of abelian and quadratic differentials., J. Mod. Dyn., 2 (2008), 139.
doi: 10.3934/jmd.2008.2.139. |
show all references
References:
[1] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture,, Acta Math., 198 (2007), 1.
doi: 10.1007/s11511-007-0012-1. |
[2] |
C. Boissy, Classification of Rauzy classes in the moduli space of quadratic differentials,, Discrete and Continuous Dynam. Systems - A, 32 (2012), 3433.
doi: 10.3934/dcds.2012.32.3433. |
[3] |
C. Boissy, Labeled rauzy classes and framed translation surfaces,, Annales de L'Institut Fourier, 63 (2013), 547.
doi: 10.5802/aif.2769. |
[4] |
C. Boissy, A combinatorial move on the set of jenkins-strebel differentials,, preprint, (). Google Scholar |
[5] |
C. Boissy and E. Lanneau, Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials,, Ergodic Theory Dynam. Systems, 29 (2009), 767.
doi: 10.1017/S0143385708080565. |
[6] |
D. Chen and M. Möller, Quadratic differentials in low genus: Exceptional and non-varying,, Annales scientifiques de l'École normale supérieure, 47 (2014), 309.
|
[7] |
V. Delecroix, Cardinality of Rauzy classes,, Annales de l'institute Fourier, 63 (2013), 1651.
doi: 10.5802/aif.2811. |
[8] |
J. Fickenscher, Self-inverses in Rauzy Classes,, Ph.D thesis, (2011).
|
[9] |
J. Fickenscher, Labeled and non-labeled extended Rauzy classes,, preprint, (). Google Scholar |
[10] |
J. Fickenscher, Self-inverses, Lagrangian permutations and minimal interval exchange transformations with many ergodic measures,, Comm. in Contemporary Mathematics, 16 (2014).
doi: 10.1142/s0219199713500193. |
[11] |
M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities,, Invent. Math., 153 (2003), 631.
doi: 10.1007/s00222-003-0303-x. |
[12] |
E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials,, Annales scientifiques de l'École normale supérieure, 41 (2008), 1.
|
[13] |
G. Rauzy, Échanges d'intervalles et transformations induites,, Acta Arith., 34 (1979), 315.
|
[14] |
W. A. Veech, Gauss measures for transformations on the space of interval exchange maps,, Ann. of Math. (2), 115 (1982), 201.
doi: 10.2307/1971391. |
[15] |
W. A. Veech, Moduli spaces of quadratic differentials,, J. Analyse Math., 55 (1990), 117.
doi: 10.1007/BF02789200. |
[16] |
M. Viana, Ergodic theory of interval exchange maps,, Rev. Mat. Complut., 19 (2006), 7.
doi: 10.5209/rev_rema.2006.v19.n1.16621. |
[17] |
A. Zorich, Explicit Jenkins-Strebel representatives of all strata of abelian and quadratic differentials., J. Mod. Dyn., 2 (2008), 139.
doi: 10.3934/jmd.2008.2.139. |
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