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Integrability and Lyapunov exponents
The Khinchin Theorem for interval-exchange transformations
1. | Section de mathématiques, case postale 64, 2–4 Rue du Lièvre, 1211 Genève, Switzerland |
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. J.Resende, Exponential mixing for the Teichmüller flow in the space of quadratic differentials,, preprint \arXiv{0908.1102}., ().
|
[3] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture, Acta Mathematica, 198 (2007), 1-56.
doi: 10.1007/s11511-007-0012-1. |
[4] |
P. Billingsley, Probability and measure, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1979. |
[5] |
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. |
[6] |
M. Boshernitzan, Rank two interval-exchange transformations, Ergodic Theory Dynam. Systems, 8 (1988), 379-394. |
[7] |
M. Boshernitzan and J. Chaika, Diophantine properties of IET and general systems: Quantitative proximality and connectivity,, preprint \arXiv{0910.5422}., ().
|
[8] |
J. Chaika, Shrinking targets for IETs: Extending a theorem of Kurzweil,, preprint \arXiv{0910.2694}., ().
|
[9] |
C. Danthony and A. Nogueira, Involutions linéaires et feuilletages mesurés, (French) [Linear involutions and measured foliations], C. R. Acad. Sci. Paris Sér I Math., 307(1988), 409-412. |
[10] |
G. H. Hardy and E. M. Wright, "An introduction to the Theory of Numbers,'' 3rd ed., Oxford, at the Clarendon Press, 1954. |
[11] |
M. Keane, Interval-exchange transformations, Math. Z., 141 (2002), 25-31.
doi: 10.1007/BF01236981. |
[12] |
S. P. Kerckhoff, Symplicial systems for interval-exchange maps and measured foliations, Ergodic Theory Dynam Systems, 5 (1985), 257-271.
doi: 10.1017/S0143385700002881. |
[13] |
Khinchin, "Continued Fractions,'' Translated by Peter Wynn. P. Noordhoff, Ltd., Groningen 1963 iii+101 pp. |
[14] |
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. |
[15] |
L. Marchese, "The Khinchin Theorem for Intervals Exchange Transformations and its Consequences for the Teichmüller Flow,'', PhD thesis., ().
|
[16] |
L. Marchese, Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow,, to appear in Bull. Soc. Math. France., ().
|
[17] |
S. Marmi, P. Moussa and J.-C.Yoccoz, The cohomological equation for Roth type interval-exchange maps, J. American Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[18] |
H. Masur, Interval exchange transformation and measured foliations, Ann. of Math. (2) , 115 (1982), 169-200,.
doi: 10.2307/1971341. |
[19] |
H. Masur, Logarithmic law for geodesic in moduli space, Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), 229-245, Contemp. Math., 150, Amer. Math. Soc., Providence, RI, 1993. |
[20] |
G. Rauzy, Échanges d'intervalles et transformations induites, (French) Acta Arith., 34 (1979), 315-328. |
[21] |
W. Veech, Interval exchange transformations, J. Analyse Math., 33 (1978), 222-272.
doi: 10.1007/BF02790174. |
[22] |
W. Veech, Gauss measures for transformations on the space of interval-exchange maps, Annals of Mathematics (2), 115 (1982), 201-242.
doi: 10.2307/1971391. |
[23] |
J.-C. Yoccoz, "Echanges d'Intervalles,'' Cours Coll\`ege de France, Janvier-Mars, 2005. |
[24] |
J.-C. Yoccoz, Interval-exchange maps and translation surfaces, CMI summer school course, Centro di ricerca matematica Ennio de Giorgi, Pisa, June-July 2007 (in preparation). |
[25] |
A. Zorich, Finite Gauss measure on the space of interval-exchange transformations. Lyapunov exponents, Annales de l'Institut Fourier (Grenoble), 46 (1996), 325-370. |
[26] |
A. Zorich, Flat surfaces, Frontiers in Number Theory, Physics and Geometry, Vol. 1, 437-583, Springer, Berlin, (2006). |
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. J.Resende, Exponential mixing for the Teichmüller flow in the space of quadratic differentials,, preprint \arXiv{0908.1102}., ().
|
[3] |
A. Avila and M. Viana, Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture, Acta Mathematica, 198 (2007), 1-56.
doi: 10.1007/s11511-007-0012-1. |
[4] |
P. Billingsley, Probability and measure, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1979. |
[5] |
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. |
[6] |
M. Boshernitzan, Rank two interval-exchange transformations, Ergodic Theory Dynam. Systems, 8 (1988), 379-394. |
[7] |
M. Boshernitzan and J. Chaika, Diophantine properties of IET and general systems: Quantitative proximality and connectivity,, preprint \arXiv{0910.5422}., ().
|
[8] |
J. Chaika, Shrinking targets for IETs: Extending a theorem of Kurzweil,, preprint \arXiv{0910.2694}., ().
|
[9] |
C. Danthony and A. Nogueira, Involutions linéaires et feuilletages mesurés, (French) [Linear involutions and measured foliations], C. R. Acad. Sci. Paris Sér I Math., 307(1988), 409-412. |
[10] |
G. H. Hardy and E. M. Wright, "An introduction to the Theory of Numbers,'' 3rd ed., Oxford, at the Clarendon Press, 1954. |
[11] |
M. Keane, Interval-exchange transformations, Math. Z., 141 (2002), 25-31.
doi: 10.1007/BF01236981. |
[12] |
S. P. Kerckhoff, Symplicial systems for interval-exchange maps and measured foliations, Ergodic Theory Dynam Systems, 5 (1985), 257-271.
doi: 10.1017/S0143385700002881. |
[13] |
Khinchin, "Continued Fractions,'' Translated by Peter Wynn. P. Noordhoff, Ltd., Groningen 1963 iii+101 pp. |
[14] |
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. |
[15] |
L. Marchese, "The Khinchin Theorem for Intervals Exchange Transformations and its Consequences for the Teichmüller Flow,'', PhD thesis., ().
|
[16] |
L. Marchese, Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow,, to appear in Bull. Soc. Math. France., ().
|
[17] |
S. Marmi, P. Moussa and J.-C.Yoccoz, The cohomological equation for Roth type interval-exchange maps, J. American Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[18] |
H. Masur, Interval exchange transformation and measured foliations, Ann. of Math. (2) , 115 (1982), 169-200,.
doi: 10.2307/1971341. |
[19] |
H. Masur, Logarithmic law for geodesic in moduli space, Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), 229-245, Contemp. Math., 150, Amer. Math. Soc., Providence, RI, 1993. |
[20] |
G. Rauzy, Échanges d'intervalles et transformations induites, (French) Acta Arith., 34 (1979), 315-328. |
[21] |
W. Veech, Interval exchange transformations, J. Analyse Math., 33 (1978), 222-272.
doi: 10.1007/BF02790174. |
[22] |
W. Veech, Gauss measures for transformations on the space of interval-exchange maps, Annals of Mathematics (2), 115 (1982), 201-242.
doi: 10.2307/1971391. |
[23] |
J.-C. Yoccoz, "Echanges d'Intervalles,'' Cours Coll\`ege de France, Janvier-Mars, 2005. |
[24] |
J.-C. Yoccoz, Interval-exchange maps and translation surfaces, CMI summer school course, Centro di ricerca matematica Ennio de Giorgi, Pisa, June-July 2007 (in preparation). |
[25] |
A. Zorich, Finite Gauss measure on the space of interval-exchange transformations. Lyapunov exponents, Annales de l'Institut Fourier (Grenoble), 46 (1996), 325-370. |
[26] |
A. Zorich, Flat surfaces, Frontiers in Number Theory, Physics and Geometry, Vol. 1, 437-583, Springer, Berlin, (2006). |
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