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Noninvertible cocycles: Robustness of exponential dichotomies
Inducing and unique ergodicity of double rotations
1. | Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom |
References:
[1] |
M. Barnsley, "Fractals Everywhere,'' Academic Press Inc., 1988. |
[2] |
G. Birkhoff, Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc., 85 (1957), 219-227.
doi: 10.2307/1992971. |
[3] |
M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergod. Th. Dyn. Sys., 15 (1995), 821-831.
doi: 10.1017/S0143385700009652. |
[4] |
H. Bruin and S. Troubetzkoy, The Gauss map on a class of interval translation mappings, Israel J. Math., 137 (2003), 125-148.
doi: 10.1007/BF02785958. |
[5] |
J. Buzzi and P. Hubert, Piecewise monotone maps without periodic points: Rigidity, measures and complexity, Ergodic Theory Dynam. Systems, 24 (2004), 383-405.
doi: 10.1017/S0143385703000488. |
[6] |
M. Keane, Non-ergodic interval exchange transformations, Israel J. Math., 26 (1977), 188-196.
doi: 10.1007/BF03007668. |
[7] |
H. B. Keynes and D. Newton, A "minimal'', non-uniquely ergodic interval exchange transformation, Math. Z., 148 (1976), 101-105.
doi: 10.1007/BF01214699. |
[8] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,'' Springer-Verlag, 1987. |
[9] |
H. Masur, Interval exchange transformations and measured foliations, Ann. of Math., 115 (1982), 169-200.
doi: 10.2307/1971341. |
[10] |
W. de Melo and S. van Strien, "One-Dimensional Dynamics,'' Springer-Verlag, 1996. |
[11] |
H. Suzuki, S. Ito and K. Aihara, Double rotations, Discrete Contin. Dyn. Sys., 13 (2005), 515-532.
doi: 10.3934/dcds.2005.13.515. |
[12] |
J. Schmeling and S. Troubetzkoy, Interval translation mappings, in "Dynamical Systems From Crystals to Chaos,'' J.-M. Gambaudo et al. eds., World Scientific, Singapore, 2000, 291-302. |
[13] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math., 115 (1982), 201-242.
doi: 10.2307/1971391. |
show all references
References:
[1] |
M. Barnsley, "Fractals Everywhere,'' Academic Press Inc., 1988. |
[2] |
G. Birkhoff, Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc., 85 (1957), 219-227.
doi: 10.2307/1992971. |
[3] |
M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergod. Th. Dyn. Sys., 15 (1995), 821-831.
doi: 10.1017/S0143385700009652. |
[4] |
H. Bruin and S. Troubetzkoy, The Gauss map on a class of interval translation mappings, Israel J. Math., 137 (2003), 125-148.
doi: 10.1007/BF02785958. |
[5] |
J. Buzzi and P. Hubert, Piecewise monotone maps without periodic points: Rigidity, measures and complexity, Ergodic Theory Dynam. Systems, 24 (2004), 383-405.
doi: 10.1017/S0143385703000488. |
[6] |
M. Keane, Non-ergodic interval exchange transformations, Israel J. Math., 26 (1977), 188-196.
doi: 10.1007/BF03007668. |
[7] |
H. B. Keynes and D. Newton, A "minimal'', non-uniquely ergodic interval exchange transformation, Math. Z., 148 (1976), 101-105.
doi: 10.1007/BF01214699. |
[8] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,'' Springer-Verlag, 1987. |
[9] |
H. Masur, Interval exchange transformations and measured foliations, Ann. of Math., 115 (1982), 169-200.
doi: 10.2307/1971341. |
[10] |
W. de Melo and S. van Strien, "One-Dimensional Dynamics,'' Springer-Verlag, 1996. |
[11] |
H. Suzuki, S. Ito and K. Aihara, Double rotations, Discrete Contin. Dyn. Sys., 13 (2005), 515-532.
doi: 10.3934/dcds.2005.13.515. |
[12] |
J. Schmeling and S. Troubetzkoy, Interval translation mappings, in "Dynamical Systems From Crystals to Chaos,'' J.-M. Gambaudo et al. eds., World Scientific, Singapore, 2000, 291-302. |
[13] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math., 115 (1982), 201-242.
doi: 10.2307/1971391. |
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