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Polynomial loss of memory for maps of the interval with a neutral fixed point
| 1. | Aix Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France, France |
| 2. | Department of Mathematics, Michigan State University, East Lansing, MI 48824 |
| 3. | Department of Mathematics, University of Houston, Houston, TX 77204-3008 |
References:
| [1] |
R. Aimino, Vitesse de mélange et théorèmes limites pour les systèmes dynamiques aléatoires et non-autonomes, Ph. D. Thesis, Université du Sud Toulon Var, (2014). |
| [2] |
R. Aimino and J. Rousseau, Concentration inequalities for sequential dynamical systems of the unit interval, preprint. |
| [3] |
W. Bahsoun, Ch. Bose and Y. Duan, Decay of correlation for random intermittent maps, Nonlinearity, 27 (2014), 1543-1554. arXiv:1305.6588.
doi: 10.1088/0951-7715/27/7/1543. |
| [4] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0, 1], Ergodic theory and related fields, Contemp. Math., Amer. Math. Soc., Providence, RI, 430 (2007), 89-121.
doi: 10.1090/conm/430/08253. |
| [5] |
W. de Melo, S. van Strien, One-dimensional Dynamics, Springer, Berlin, 1993. |
| [6] |
S. Gouëzel, Central limit theorem and stable laws for intermittent maps, Probab. Theory Relat. Fields, 128 (2004), 82-122,
doi: 10.1007/s00440-003-0300-4. |
| [7] |
C. Gupta, W. Ott and A. Török, Memory loss for time-dependent piecewise expanding systems in higher dimension, Mathematical Research Letters, 20 (2013), 141-161.
doi: 10.4310/MRL.2013.v20.n1.a12. |
| [8] |
H. Hu, Decay of correlations for piecewise smooth maps with indifferent fixed points, Ergodic Theory and Dynamical Systems, 24 (2004), 495-524.
doi: 10.1017/S0143385703000671. |
| [9] |
C. Liverani, B. Saussol and S. Vaienti, A probabilistic approach to intermittency, Ergodic theory and dynamical systems, 19 (1999), 671-685.
doi: 10.1017/S0143385799133856. |
| [10] |
W. Ott, M. Stenlund and L.-S. Young, Memory loss for time-dependent dynamical systems, Math. Res. Lett., 16 (2009), 463-475.
doi: 10.4310/MRL.2009.v16.n3.a7. |
| [11] |
O. Sarig, Subexponential decay of correlations, Invent. Math., 150 (2002), 629-653.
doi: 10.1007/s00222-002-0248-5. |
| [12] |
W. Shen and S. Van Strien, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems, An International Journal, 28 (2013), 423-452.
doi: 10.1080/14689367.2013.806733. |
| [13] |
M. Stenlund, Non-stationary compositions of Anosov diffeomorphisms, Nonlinearity, 24 (2011), 2991-3018.
doi: 10.1088/0951-7715/24/10/016. |
| [14] |
M. Stenlund, L-S. Young and H. Zhang, Dispersing billiards with moving scatterers, Comm. Math. Phys., 322 (2013), 909-955.
doi: 10.1007/s00220-013-1746-6. |
show all references
References:
| [1] |
R. Aimino, Vitesse de mélange et théorèmes limites pour les systèmes dynamiques aléatoires et non-autonomes, Ph. D. Thesis, Université du Sud Toulon Var, (2014). |
| [2] |
R. Aimino and J. Rousseau, Concentration inequalities for sequential dynamical systems of the unit interval, preprint. |
| [3] |
W. Bahsoun, Ch. Bose and Y. Duan, Decay of correlation for random intermittent maps, Nonlinearity, 27 (2014), 1543-1554. arXiv:1305.6588.
doi: 10.1088/0951-7715/27/7/1543. |
| [4] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0, 1], Ergodic theory and related fields, Contemp. Math., Amer. Math. Soc., Providence, RI, 430 (2007), 89-121.
doi: 10.1090/conm/430/08253. |
| [5] |
W. de Melo, S. van Strien, One-dimensional Dynamics, Springer, Berlin, 1993. |
| [6] |
S. Gouëzel, Central limit theorem and stable laws for intermittent maps, Probab. Theory Relat. Fields, 128 (2004), 82-122,
doi: 10.1007/s00440-003-0300-4. |
| [7] |
C. Gupta, W. Ott and A. Török, Memory loss for time-dependent piecewise expanding systems in higher dimension, Mathematical Research Letters, 20 (2013), 141-161.
doi: 10.4310/MRL.2013.v20.n1.a12. |
| [8] |
H. Hu, Decay of correlations for piecewise smooth maps with indifferent fixed points, Ergodic Theory and Dynamical Systems, 24 (2004), 495-524.
doi: 10.1017/S0143385703000671. |
| [9] |
C. Liverani, B. Saussol and S. Vaienti, A probabilistic approach to intermittency, Ergodic theory and dynamical systems, 19 (1999), 671-685.
doi: 10.1017/S0143385799133856. |
| [10] |
W. Ott, M. Stenlund and L.-S. Young, Memory loss for time-dependent dynamical systems, Math. Res. Lett., 16 (2009), 463-475.
doi: 10.4310/MRL.2009.v16.n3.a7. |
| [11] |
O. Sarig, Subexponential decay of correlations, Invent. Math., 150 (2002), 629-653.
doi: 10.1007/s00222-002-0248-5. |
| [12] |
W. Shen and S. Van Strien, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems, An International Journal, 28 (2013), 423-452.
doi: 10.1080/14689367.2013.806733. |
| [13] |
M. Stenlund, Non-stationary compositions of Anosov diffeomorphisms, Nonlinearity, 24 (2011), 2991-3018.
doi: 10.1088/0951-7715/24/10/016. |
| [14] |
M. Stenlund, L-S. Young and H. Zhang, Dispersing billiards with moving scatterers, Comm. Math. Phys., 322 (2013), 909-955.
doi: 10.1007/s00220-013-1746-6. |
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