Comptes Rendus
no. 11
Dynamical systems
Exponential decay of correlations for a real-valued dynamical system embedded in R2
Presented by: the Editorial Board
Lisette Jager1; Jules Maes1; Alain Ninet1
1 Laboratoire de mathématiques, FR CNRS 3399, EA 4535, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1041-1045

We study the real valued process {Xt,t∈N} defined by Xt+2=φ(Xt,Xt+1), where the Xt are bounded. We aim at proving the decay of correlations for this model, under regularity assumptions on the transformation φ.

On étudie le processus réel {Xt,t∈N} défini par Xt+2=φ(Xt,Xt+1), les Xt étant bornés. Sous des hypothèses de régularité sur la transformation φ, on établit la décroissance des corrélations pour ce modèle.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.07.015

Lisette Jager 1; Jules Maes 1; Alain Ninet 1

1 Laboratoire de mathématiques, FR CNRS 3399, EA 4535, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims, France 
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Lisette Jager; Jules Maes; Alain Ninet. Exponential decay of correlations for a real-valued dynamical system embedded in $ {\mathbb{R}}^{2}$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1041-1045. doi: 10.1016/j.crma.2015.07.015

[1] J.F. Alves; J.M. Freitas; S. Luzatto; S. Vaienti From rates of mixing to recurrence times via large deviations, Adv. Math., Volume 228 (2011) no. 2, pp. 1203-1236

[2] P. Collet; J.-P. Eckmann Concepts and Results in Chaotic Dynamics: A Short Course, Theoretical and Mathematical Physics, Springer-Verlag, Berlin, 2006

[3] F. Hofbauer; G. Keller Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z., Volume 180 (1982), pp. 119-140

[4] C.T. Ionescu Tulcea; G. Marinescu Théorie ergodique pour des classes d'opérations non complètement continues, Ann. of Math. (2), Volume 52 (1950), pp. 140-147

[5] A. Lasota; M.C. Mackey Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer Verlag, New York, 1998

[6] C. Liverani Multidimensional expanding maps with singularities: a pedestrian approach, Ergod. Theory Dyn. Syst., Volume 33 (2013) no. 1, pp. 168-182

[7] B. Saussol Absolutely continuous invariant measures for multidimensional expanding maps, Isr. J. Math., Volume 116 (2000), pp. 223-248

[8] H. Tong Nonlinear Time Series: A Dynamical System Approach (with an appendix by K.S. Chan), Oxford Statistical Science Series, vol. 6, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1990

[9] H. Tong Nonlinear time series analysis since 1990: some personal reflections, Acta Math. Appl. Sin. Engl. Ser., Volume 18 (2002) no. 2, pp. 177-184

[10] L.-S. Young Recurrence times and rates of mixing, Isr. J. Math., Volume 110 (1999), pp. 153-188

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