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Inverting the Furstenberg correspondence
Classification of Rauzy classes in the moduli space of Abelian and quadratic differentials
1. | Aix-Marseille Université LATP, case cour A, Faculté des Sciences de Saint Jerôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille cedex 20, France |
References:
[1] |
A. Avila, S. Gouëzel and J.-C. Yoccoz, Exponential mixing for the Teichmüller flow, Publ. Math. Inst. Hautes Études Sci., 104 (2006), 143-211. |
[2] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture, Acta Math., 198 (2007), 1-56. |
[3] |
C. Boissy, Configurations of saddle connections of quadratic differentials on $\mathbb{CP}^1$ and on hyperelliptic Riemann surfaces, Comment. Math. Helv., 84 (2009), 757-791.
doi: 10.4171/CMH/180. |
[4] |
C. Boissy, Degenerations of quadratic differentials on $\mathbb{CP}^1$, Geometry and Topology, 12 (2008), 1345-1386.
doi: 10.2140/gt.2008.12.1345. |
[5] |
C. Boissy, Labeled Rauzy classes and framed translation surfaces, to appear in Annales de l'Institut Fourier, 2010, arXiv:1010.5719. |
[6] |
C. Boissy and E. Lanneau, Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials, Ergodic Theory Dynam. Systems, 29 (2009), 767-816.
doi: 10.1017/S0143385708080565. |
[7] |
C. Danthony and A. Nogueira, Measured foliations on nonorientable surfaces, Ann. Sci. École Norm. Sup. (4), 23 (1990), 469-494. |
[8] |
A. Douady and J. Hubbard, On the density of Strebel differentials, Inventiones Math., 30 (1975), 175-179.
doi: 10.1007/BF01425507. |
[9] |
A. Eskin, H. Masur and A. Zorich, Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel-Veech constants, Publ. Math. Hautes Études Sci., 97 (2003), 61-179. |
[10] |
J. Fickenscher, Self-inverses in Rauzy classes, preprint, 2011, arXiv:1103.3485. |
[11] |
A. Katok, Interval exchange transformations and some special flows are not mixing, Israel J. Math., 35 (1980), 301-310.
doi: 10.1007/BF02760655. |
[12] |
M. Keane, Interval exchange transformations, Math. Zeit., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[13] |
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. |
[14] |
E. Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities, Comment. Math. Helv., 79 (2004), 471-501. |
[15] |
E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials, Ann. Sci. École Norm. Sup. (4), 41 (2008), 1-56. |
[16] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The cohomological equation for Roth type interval exchange maps, Journal of the Amer. Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[17] |
H. Masur, Interval exchange transformations and measured foliations, Ann of Math. (2), 115 (1982), 169-200.
doi: 10.2307/1971341. |
[18] |
H. Masur and J. Smillie, Quadratic differentials with prescribed singularities and pseudo-Anosov homeomorphisms, Comment. Math. Helv., 68 (1993), 289-307.
doi: 10.1007/BF02565820. |
[19] |
H. Masur and S. Tabachnikov, Rational billiards and flat structures, IN "Handbook of Dynamical Systems," Vol. 1A, North-Holland, Amsterdam, (2002), 1015-1089. |
[20] |
H. Masur and A. Zorich, Multiple saddle connections on flat surfaces and the principal boundary of the moduli space of quadratic differentials, Geom. Funct. Anal., 18 (2008), 919-987.
doi: 10.1007/s00039-008-0678-3. |
[21] |
G. Rauzy, Échanges d'intervalles et transformations induites, Acta Arith., 34 (1979), 315-328. |
[22] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2), 115 (1982), 201-242.
doi: 10.2307/1971391. |
[23] |
W. Veech, Moduli spaces of quadratic differentials, J. Analyse Math., 55 (1990), 117-171.
doi: 10.1007/BF02789200. |
[24] |
A. Zorich, Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials, Journal of Modern Dynamics, 2 (2008), 139-185. |
show all references
References:
[1] |
A. Avila, S. Gouëzel and J.-C. Yoccoz, Exponential mixing for the Teichmüller flow, Publ. Math. Inst. Hautes Études Sci., 104 (2006), 143-211. |
[2] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture, Acta Math., 198 (2007), 1-56. |
[3] |
C. Boissy, Configurations of saddle connections of quadratic differentials on $\mathbb{CP}^1$ and on hyperelliptic Riemann surfaces, Comment. Math. Helv., 84 (2009), 757-791.
doi: 10.4171/CMH/180. |
[4] |
C. Boissy, Degenerations of quadratic differentials on $\mathbb{CP}^1$, Geometry and Topology, 12 (2008), 1345-1386.
doi: 10.2140/gt.2008.12.1345. |
[5] |
C. Boissy, Labeled Rauzy classes and framed translation surfaces, to appear in Annales de l'Institut Fourier, 2010, arXiv:1010.5719. |
[6] |
C. Boissy and E. Lanneau, Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials, Ergodic Theory Dynam. Systems, 29 (2009), 767-816.
doi: 10.1017/S0143385708080565. |
[7] |
C. Danthony and A. Nogueira, Measured foliations on nonorientable surfaces, Ann. Sci. École Norm. Sup. (4), 23 (1990), 469-494. |
[8] |
A. Douady and J. Hubbard, On the density of Strebel differentials, Inventiones Math., 30 (1975), 175-179.
doi: 10.1007/BF01425507. |
[9] |
A. Eskin, H. Masur and A. Zorich, Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel-Veech constants, Publ. Math. Hautes Études Sci., 97 (2003), 61-179. |
[10] |
J. Fickenscher, Self-inverses in Rauzy classes, preprint, 2011, arXiv:1103.3485. |
[11] |
A. Katok, Interval exchange transformations and some special flows are not mixing, Israel J. Math., 35 (1980), 301-310.
doi: 10.1007/BF02760655. |
[12] |
M. Keane, Interval exchange transformations, Math. Zeit., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[13] |
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. |
[14] |
E. Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities, Comment. Math. Helv., 79 (2004), 471-501. |
[15] |
E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials, Ann. Sci. École Norm. Sup. (4), 41 (2008), 1-56. |
[16] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The cohomological equation for Roth type interval exchange maps, Journal of the Amer. Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[17] |
H. Masur, Interval exchange transformations and measured foliations, Ann of Math. (2), 115 (1982), 169-200.
doi: 10.2307/1971341. |
[18] |
H. Masur and J. Smillie, Quadratic differentials with prescribed singularities and pseudo-Anosov homeomorphisms, Comment. Math. Helv., 68 (1993), 289-307.
doi: 10.1007/BF02565820. |
[19] |
H. Masur and S. Tabachnikov, Rational billiards and flat structures, IN "Handbook of Dynamical Systems," Vol. 1A, North-Holland, Amsterdam, (2002), 1015-1089. |
[20] |
H. Masur and A. Zorich, Multiple saddle connections on flat surfaces and the principal boundary of the moduli space of quadratic differentials, Geom. Funct. Anal., 18 (2008), 919-987.
doi: 10.1007/s00039-008-0678-3. |
[21] |
G. Rauzy, Échanges d'intervalles et transformations induites, Acta Arith., 34 (1979), 315-328. |
[22] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2), 115 (1982), 201-242.
doi: 10.2307/1971391. |
[23] |
W. Veech, Moduli spaces of quadratic differentials, J. Analyse Math., 55 (1990), 117-171.
doi: 10.1007/BF02789200. |
[24] |
A. Zorich, Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials, Journal of Modern Dynamics, 2 (2008), 139-185. |
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