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Springer-Verlag, New York-Berlin, 1983.","DOI":"10.1007\/978-1-4612-5449-2"},{"key":"54","unstructured":"[54] V. G. Sprindzuk. <i>Metric Theory of Diophantine Approximations. Scripta Series in Mathematics<\/i>. V. H. Winston and Sons, Washington, D.C., 1979. Translated from the Russian and edited by Richard A. Silverman. With a foreword by Donald J. Newman."},{"key":"59","doi-asserted-by":"crossref","unstructured":"[59] J.-C. Yoccoz. Continued fraction algorithms for interval exchange maps: An introduction. In <i>Frontiers in Number Theory, Physics, and Geometry. I<\/i> 401\u2013435. Springer, Berlin, 2006.","DOI":"10.1007\/978-3-540-31347-2_12"},{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] J. Aaronson. <i>An Introduction to Infinite Ergodic Theory. Mathematical Surveys and Monographs<\/i> <b>50<\/b>. AMS, Providence, 1997.","DOI":"10.1090\/surv\/050"},{"key":"2","unstructured":"[2] M. Abadi and A. Galves. Inequalities for the occurrence times of rare events in mixing processes. The state of the art. <i>Markov Process. Related Fields<\/i> <b>7<\/b> (2001) 97\u2013112."},{"key":"3","doi-asserted-by":"crossref","unstructured":"[3] J. Athreya. Quantitative recurrence and large deviations for Teichm\u00fcller geodesic flow. <i>Geom. Dedicata<\/i> <b>119<\/b> (2006) 121\u2013140.","DOI":"10.1007\/s10711-006-9058-z"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] A. Avila and A. Bufetov. Exponential decay of correlations for the Rauzy\u2013Veech\u2013Zorich induction map. In <i>Partially Hyperbolic Dynamics, Laminations, and Teichm\u00fcller Flow<\/i> 203\u2013211. <i>Fields Inst. Commun.<\/i> <b>51<\/b>. Amer. Math. Soc., Providence, RI, 2007.","DOI":"10.1090\/fic\/051\/08"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] A. Avila, S. Gou\u00ebzel and J.-C. Yoccoz. Exponential mixing of the Teichm\u00fcller flow. <i>Publ. Math. Inst. Hautes Etudes Sci.<\/i> <b>104<\/b> (2006) 143\u2013211.","DOI":"10.1007\/s10240-006-0001-5"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] H. Ayta\u00e7, J. M. Freitas and S. Vaienti. Laws of rare events for deterministic and random dynamical systems. <i>Trans. Amer. Math. Soc.<\/i> <b>367<\/b> (2015) 8229\u20138278.","DOI":"10.1090\/S0002-9947-2014-06300-9"},{"key":"7","doi-asserted-by":"crossref","unstructured":"[7] V. Baladi. <i>Positive Transfer Operators and Decay of Correlations. Advanced Series in Nonlinear Dynamics<\/i> <b>16<\/b>. World Scientific, River Edge, 2000.","DOI":"10.1142\/3657"},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] H. Bruin, B. Saussol, S. Troubetzkoy and S. Vaienti. Return time statistics via inducing. <i>Ergodic Theory Dynam. Systems<\/i> <b>23<\/b> (2003) 991\u20131013.","DOI":"10.1017\/S0143385703000026"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] A. Bufetov. Decay of correlations for the Rauzy\u2013Veech\u2013Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichm\u00fcller flow on the moduli space of abelian differentials. <i>J. Amer. Math. Soc.<\/i> <b>19<\/b> (2006) 579\u2013623.","DOI":"10.1090\/S0894-0347-06-00528-5"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] A. I. Bufetov and B. M. Gurevich. Existence and uniqueness of a measure with maximal entropy for the Teichm\u00fcller flow on the moduli space of abelian differentials. <i>Mat. Sb.<\/i> <b>202<\/b> (2011) 3\u201342.","DOI":"10.1070\/SM2011v202n07ABEH004172"},{"key":"11","doi-asserted-by":"crossref","unstructured":"[11] N. Chernov and D. Kleinbock. Dynamical Borel\u2013Cantelli lemmas for Gibbs measures. <i>Israel J. Math.<\/i> <b>122<\/b> (2001) 1\u201327.","DOI":"10.1007\/BF02809888"},{"key":"12","doi-asserted-by":"crossref","unstructured":"[12] P. Collet. Statistics of closest return for some non-uniformly hyperbolic systems. <i>Ergodic Theory Dynam. Systems<\/i> <b>21<\/b> (2001) 401\u2013420.","DOI":"10.1017\/S0143385701001201"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[13] D. Dolgopyat. Limit theorems for partially hyperbolic systems. <i>Trans. Amer. Math. Soc.<\/i> <b>356<\/b> (2004) 1637\u20131689.","DOI":"10.1090\/S0002-9947-03-03335-X"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] M. Einsiedler and T. Ward. <i>Ergodic Theory with a View Towards Number Theory. Graduate Texts in Mathematics<\/i> <b>259<\/b>. Springer, London, 2011.","DOI":"10.1007\/978-0-85729-021-2"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] A. C. M. Freitas, J. M. Freitas and M. Todd. Hitting time statistics and extreme value theory. <i>Probab. Theory Related Fields<\/i> <b>147<\/b> (2010) 675\u2013710.","DOI":"10.1007\/s00440-009-0221-y"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] A. C. M. Freitas, J. M. Freitas and M. Todd. The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics. <i>Comm. Math. Phys.<\/i> <b>321<\/b> (2013) 483\u2013527.","DOI":"10.1007\/s00220-013-1695-0"},{"key":"17","doi-asserted-by":"crossref","unstructured":"[17] A. C. M. Freitas, J. M. Freitas, M. Todd and S. Vaienti. Rare events for the Manneville\u2013Pomeau map. <i>Stochastic Process. Appl.<\/i> <b>126<\/b> (11) (2016) 3463\u20133479.","DOI":"10.1016\/j.spa.2016.05.001"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] S. Galatolo. Dimension and hitting time in rapidly mixing systems. <i>Math. Res. Lett.<\/i> <b>14<\/b> (5) (2007) 797\u2013805.","DOI":"10.4310\/MRL.2007.v14.n5.a8"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] S. Galatolo and D. Kim. The dynamical Borel\u2013Cantelli lemma and the waiting time problems. <i>Indag. Math. (N.S.)<\/i> <b>18<\/b> (3) (2007) 421\u2013434.","DOI":"10.1016\/S0019-3577(07)80031-0"},{"key":"20","doi-asserted-by":"crossref","unstructured":"[20] S. Gou\u00ebzel. Sharp polynomial estimates for the decay of correlations. <i>Israel J. Math.<\/i> <b>139<\/b> (2004) 29\u201365.","DOI":"10.1007\/BF02787541"},{"key":"21","doi-asserted-by":"crossref","unstructured":"[21] S. Gou\u00ebzel. A Borel\u2013Cantelli lemma for intermittent interval maps. <i>Nonlinearity<\/i> <b>20<\/b> (6) (2007) 1491\u20131497.","DOI":"10.1088\/0951-7715\/20\/6\/010"},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] S. Gou\u00ebzel. Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences. <i>Duke Math. J.<\/i> <b>147<\/b> (2009) 192\u2013284.","DOI":"10.1215\/00127094-2009-011"},{"key":"23","doi-asserted-by":"crossref","unstructured":"[23] C. Gupta. Extreme value distributions for some classes of non-uniformly partially hyperbolic dynamical systems. <i>Ergodic Theory Dynam. Systems<\/i> <b>30<\/b> (2010) 757\u2013771.","DOI":"10.1017\/S0143385709000406"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] C. Gupta, M. Holland and M. Nicol. Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. <i>Ergodic Theory Dynam. Systems<\/i> <b>31<\/b> (2011) 1363\u20131390.","DOI":"10.1017\/S014338571000057X"},{"key":"25","doi-asserted-by":"crossref","unstructured":"[25] C. Gupta, M. Nicol and W. Ott. A Borel\u2013Cantelli lemma for non-uniformly expanding dynamical systems. <i>Nonlinearity<\/i> <b>23<\/b> (2010) 1991\u20132008.","DOI":"10.1088\/0951-7715\/23\/8\/010"},{"key":"26","doi-asserted-by":"crossref","unstructured":"[26] N. Haydn, Y. Lacroix and S. Vaienti. Hitting and return time statistics in ergodic dynamical systems. <i>Ann. Probab.<\/i> <b>33<\/b> (2005) 2043\u20132050.","DOI":"10.1214\/009117905000000242"},{"key":"27","doi-asserted-by":"crossref","unstructured":"[27] N. Haydn, M. Nicol, T. Persson and S. Vaienti. A note on Borel\u2013Cantelli lemmas for non-uniformly hyperbolic dynamical systems. <i>Ergodic Theory Dynam. Systems<\/i> <b>33<\/b> (2013) 475\u2013498.","DOI":"10.1017\/S014338571100099X"},{"key":"28","doi-asserted-by":"crossref","unstructured":"[28] N. T. Haydn, N. Winterberg and R. Zweim\u00fcller. Return-time statistics, hitting-time statistics and inducing. In <i>Ergodic theory, Open Dynamics, and Coherent Structures<\/i> 217\u2013227. <i>Springer Proceedings in Mathematics &amp; Statistics<\/i> <b>70<\/b>. Springer, New York, 2014.","DOI":"10.1007\/978-1-4939-0419-8_10"},{"key":"29","doi-asserted-by":"crossref","unstructured":"[29] H. Hennion. Sur un th\u00e9or\u00e8me spectral et son application aux noyaux lipschitziens. <i>Proc. Amer. Math. Soc.<\/i> <b>118<\/b> (1993) 627\u2013634.","DOI":"10.2307\/2160348"},{"key":"30","doi-asserted-by":"crossref","unstructured":"[30] M. Hirata. Poisson limit law for Axiom-A diffeomorphisms. <i>Ergodic Theory Dynam. Systems<\/i> <b>13<\/b> (1993) 533\u2013556.","DOI":"10.1017\/S0143385700007513"},{"key":"31","doi-asserted-by":"crossref","unstructured":"[31] M. Hirata, B. Saussol and S. Vaienti. Statistics of return times: A general framework and new applications. <i>Comm. Math. Phys.<\/i> <b>206<\/b> (1999) 33\u201355.","DOI":"10.1007\/s002200050697"},{"key":"32","doi-asserted-by":"crossref","unstructured":"[32] M. P. Holland, M. Nicol and A. T\u00f6r\u00f6k. Extreme value distributions for non-uniformly hyperbolic dynamical systems. <i>Trans. Amer. Math. Soc.<\/i> <b>364<\/b> (2012) 661\u2013688.","DOI":"10.1090\/S0002-9947-2011-05271-2"},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] S. Kalikow and R. McCutcheon. <i>An Outline of Ergodic Theory. Cambridge Studies in Advanced Mathematics<\/i> <b>122<\/b>. Cambridge University Press, Cambridge, 2010.","DOI":"10.1017\/CBO9780511801600"},{"key":"34","doi-asserted-by":"crossref","unstructured":"[34] M. Keane. Interval exchange transformations. <i>Math. Z.<\/i> <b>141<\/b> (1975) 25\u201331.","DOI":"10.1007\/BF01236981"},{"key":"35","doi-asserted-by":"crossref","unstructured":"[35] G. Keller. Generalized bounded variation and applications to piecewise monotonic transformations. <i>Z. Wahrsch. Verw. Gebiete<\/i> <b>69<\/b> (1985) 461\u2013478.","DOI":"10.1007\/BF00532744"},{"key":"36","doi-asserted-by":"crossref","unstructured":"[36] D. Kim. The dynamical Borel\u2013Cantelli lemma for interval maps. <i>Discrete Contin. Dyn. Syst.<\/i> <b>17<\/b> (4) (2007) 891\u2013900.","DOI":"10.3934\/dcds.2007.17.891"},{"key":"37","doi-asserted-by":"crossref","unstructured":"[37] D. Kleinbock and G. Margulis. Logarithm laws for flows on homogeneous spaces. <i>Invent. Math.<\/i> <b>138<\/b> (1999) 451\u2013494.","DOI":"10.1007\/s002220050350"},{"key":"39","doi-asserted-by":"crossref","unstructured":"[39] L. Marchese. The Khinchin theorem for interval-exchange transformations. <i>J. Mod. Dyn.<\/i> <b>5<\/b> (2011) 123\u2013183.","DOI":"10.3934\/jmd.2011.5.123"},{"key":"40","doi-asserted-by":"crossref","unstructured":"[40] L. Marchese. Khinchin type condition for translation surfaces and asymptotic laws for the Teichm\u00fcller flow. <i>Bull. Soc. Math. France<\/i> <b>140<\/b> (2013) 485\u2013532.","DOI":"10.24033\/bsmf.2634"},{"key":"41","doi-asserted-by":"crossref","unstructured":"[41] H. Masur. Interval exchange transformations and measured foliations. <i>Ann. of Math. (2)<\/i> <b>115<\/b> (1982) 169\u2013200.","DOI":"10.2307\/1971341"},{"key":"42","doi-asserted-by":"crossref","unstructured":"[42] H. Masur. Logarithm law for geodesics in moduli space. In <i>Mapping Class Groups and Moduli Spaces of Riemann Surfaces<\/i> 229\u2013245. <i>Comtemp. Math.<\/i> <b>150<\/b>. Amer. Math. Soc., Providence, RI, 1993.","DOI":"10.1090\/conm\/150\/01293"},{"key":"43","doi-asserted-by":"crossref","unstructured":"[43] F. Maucourant. Dynamical Borel\u2013Cantelli lemma for hyperbolic spaces. <i>Israel J. Math.<\/i> <b>152<\/b> (2006) 143\u2013155.","DOI":"10.1007\/BF02771980"},{"key":"44","doi-asserted-by":"crossref","unstructured":"[44] I. Melbourne and M. Nicol. Almost sure invariance principle for nonuniformly hyperbolic systems. <i>Comm. Math. Phys.<\/i> <b>260<\/b> (2005) 131\u2013146.","DOI":"10.1007\/s00220-005-1407-5"},{"key":"45","doi-asserted-by":"crossref","unstructured":"[45] I. Melbourne and M. Nicol. Large deviations for nonuniformly hyperbolic systems. <i>Trans. Amer. Math. Soc.<\/i> <b>360<\/b> (2008) 6661\u20136676.","DOI":"10.1090\/S0002-9947-08-04520-0"},{"key":"46","unstructured":"[46] T. Morita. A generalized local limit theorem for Lasota\u2013Yorke transformations. <i>Osaka J. Math.<\/i> <b>26<\/b> (1989) 579\u2013595."},{"key":"47","doi-asserted-by":"crossref","unstructured":"[47] T. Morita. Renormalized Rauzy inductions. <i>Adv. Stud. Pure Math.<\/i> <b>49<\/b> (2007) 263\u2013288.","DOI":"10.2969\/aspm\/04910263"},{"key":"48","doi-asserted-by":"crossref","unstructured":"[48] W. Philipp. Some metrical theorems in number theory. <i>Pacific J. Math.<\/i> <b>20<\/b> (1967) 109\u2013127.","DOI":"10.2140\/pjm.1967.20.109"},{"key":"49","unstructured":"[49] M. Pollicott. Statistical properties of the Rauzy\u2013Veech\u2013Zorich map. Unpublished notes. Available at <a href=\"http:\/\/homepages.warwick.ac.uk\/~masdbl\/teichmuller-asip.pdf\">http:\/\/homepages.warwick.ac.uk\/~masdbl\/teichmuller-asip.pdf<\/a>."},{"key":"50","doi-asserted-by":"crossref","unstructured":"[50] O. Sarig. Subexponential decay of correlations. <i>Invent. Math.<\/i> <b>150<\/b> (2002) 629\u2013653.","DOI":"10.1007\/s00222-002-0248-5"},{"key":"51","doi-asserted-by":"crossref","unstructured":"[51] B. Saussol. Absolutely continuous invariant measures for multidimensional expanding maps. <i>Israel J. Math.<\/i> <b>116<\/b> (2000) 223\u2013248.","DOI":"10.1007\/BF02773219"},{"key":"52","doi-asserted-by":"crossref","unstructured":"[52] W. Schmidt. A metrical theory in Diophantine approximation. <i>Canad. J. Math.<\/i> <b>12<\/b> (1960) 619\u2013631.","DOI":"10.4153\/CJM-1960-056-0"},{"key":"53","doi-asserted-by":"crossref","unstructured":"[53] W. Schmidt. Metrical theorems on fractional parts of sequences. <i>Trans. Amer. Math. Soc.<\/i> <b>110<\/b> (1964) 493\u2013518.","DOI":"10.1090\/S0002-9947-1964-0159802-4"},{"key":"55","doi-asserted-by":"crossref","unstructured":"[55] W. A. Veech. Gauss measures for transformations on the space of interval exchange maps. <i>Ann. of Math. (2)<\/i> <b>115<\/b> (1982) 201\u2013242.","DOI":"10.2307\/1971391"},{"key":"56","doi-asserted-by":"crossref","unstructured":"[56] W. A. Veech. The Teichm\u00fcller geodesic flow. <i>Ann. of Math. (2)<\/i> <b>124<\/b> (1986) 441\u2013530.","DOI":"10.2307\/2007091"},{"key":"57","unstructured":"[57] M. Viana. Dynamics of interval exchange maps and Teichm\u00fcller flows. IMPA, 2008. Available at <a href=\"http:\/\/w3.impa.br\/~viana\/out\/ietf.pdf\">http:\/\/w3.impa.br\/~viana\/out\/ietf.pdf<\/a>."},{"key":"58","doi-asserted-by":"crossref","unstructured":"[58] P. Walters. <i>An Introduction to Ergodic Theory. Graduate Texts in Mathematics<\/i> <b>79<\/b>. Springer, New York-Berlin, 1982.","DOI":"10.1007\/978-1-4612-5775-2"},{"key":"60","doi-asserted-by":"crossref","unstructured":"[60] L.-S. Young. Statistical properties of dynamical systems with some hyperbolicity. <i>Ann. of Math.<\/i> <b>147<\/b> (1998) 585\u2013650.","DOI":"10.2307\/120960"},{"key":"61","doi-asserted-by":"crossref","unstructured":"[61] L.-S. Young. Recurrence times and rates of mixing. <i>Israel J. Math.<\/i> <b>110<\/b> (1999) 153\u2013188.","DOI":"10.1007\/BF02808180"},{"key":"62","doi-asserted-by":"crossref","unstructured":"[62] L. Zhang. Borel\u2013Cantelli lemmas and extreme value theory for geometric Lorenz models. <i>Nonlinearity<\/i> <b>29<\/b> (1) (2016) 232\u2013255.","DOI":"10.1088\/0951-7715\/29\/1\/232"},{"key":"63","doi-asserted-by":"crossref","unstructured":"[63] A. Zorich. Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents. <i>Ann. Inst. 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