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Erratum: Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition
There exists an interval exchange with a non-ergodic generic measure
1. | Department of Mathematics, University of Utah, 155 S. 1400 E., Room 233, Salt Lake City, UT 84112 |
2. | Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, IL 60637, United States |
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.
doi: 10.1007/s10240-006-0001-5. |
[2] |
V. Cyr and B. Kra, Counting generic measures for a subshift of linear growth, arXiv:1505.02748. |
[3] |
A. B. Katok, Invariant measures of flows on orientable surfaces, Dokl. Akad. Nauk SSSR, 211 (1973), 775-778. |
[4] |
M. Keane, Interval exchange trasformations, Math. Z., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[5] |
M. Keane, Non-ergodic interval exchange transformations, Israel J. Math., 26 (1977), 188-196.
doi: 10.1007/BF03007668. |
[6] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The cohomological equation for Roth-type interval exchange maps, J. Amer. Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[7] |
H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2), 115 (1982), 169-200.
doi: 10.2307/1971341. |
[8] |
E. A. Sataev, The number of invariant measures for flows on orientable surfaces, Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 860-878. |
[9] |
M. Viana, Ergodic theory of interval exchange maps, Rev. Mat. Complut., 19 (2006), 7-100.
doi: 10.5209/rev_REMA.2006.v19.n1.16621. |
[10] |
W. Veech, A Kronecker-Weyl theorem modulo 2, Proc. Nat. Acad. Sci. U.S.A., 60 (1968), 1163-1164.
doi: 10.1073/pnas.60.4.1163. |
[11] |
W. Veech, Interval exchange transformations, J. Analyse Math., 33 (1978), 222-272.
doi: 10.1007/BF02790174. |
[12] |
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. |
[13] |
J.-C. Yoccoz, Interval exchange maps and translation surfaces, in Homogeneous Flows, Moduli Spaces and Arithmetic, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010, 1-69. |
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.
doi: 10.1007/s10240-006-0001-5. |
[2] |
V. Cyr and B. Kra, Counting generic measures for a subshift of linear growth, arXiv:1505.02748. |
[3] |
A. B. Katok, Invariant measures of flows on orientable surfaces, Dokl. Akad. Nauk SSSR, 211 (1973), 775-778. |
[4] |
M. Keane, Interval exchange trasformations, Math. Z., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[5] |
M. Keane, Non-ergodic interval exchange transformations, Israel J. Math., 26 (1977), 188-196.
doi: 10.1007/BF03007668. |
[6] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The cohomological equation for Roth-type interval exchange maps, J. Amer. Math. Soc., 18 (2005), 823-872.
doi: 10.1090/S0894-0347-05-00490-X. |
[7] |
H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2), 115 (1982), 169-200.
doi: 10.2307/1971341. |
[8] |
E. A. Sataev, The number of invariant measures for flows on orientable surfaces, Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 860-878. |
[9] |
M. Viana, Ergodic theory of interval exchange maps, Rev. Mat. Complut., 19 (2006), 7-100.
doi: 10.5209/rev_REMA.2006.v19.n1.16621. |
[10] |
W. Veech, A Kronecker-Weyl theorem modulo 2, Proc. Nat. Acad. Sci. U.S.A., 60 (1968), 1163-1164.
doi: 10.1073/pnas.60.4.1163. |
[11] |
W. Veech, Interval exchange transformations, J. Analyse Math., 33 (1978), 222-272.
doi: 10.1007/BF02790174. |
[12] |
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. |
[13] |
J.-C. Yoccoz, Interval exchange maps and translation surfaces, in Homogeneous Flows, Moduli Spaces and Arithmetic, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010, 1-69. |
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