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Polynomial loss of memory for maps of the interval with a neutral fixed point

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  • We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any sequence, and the bound holds for all compositions.
    Mathematics Subject Classification: 37E05, 37A25, 37H99, 37M99.

    Citation:

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  • [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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