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Quantitative recurrence of some dynamical systems preserving an infinite measure in dimension one

  • * Corresponding author: Nasab Yassine

    * Corresponding author: Nasab Yassine
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  • We are interested in the asymptotic behaviour of the first return time of the orbits of a dynamical system into a small neighbourhood of their starting points. We study this quantity in the context of dynamical systems preserving an infinite measure. More precisely, we consider the case of $\mathbb{Z}$-extensions of subshifts of finite type. We also consider a toy probabilistic model to enlight the strategy of our proofs.

    Mathematics Subject Classification: Primary:37B20;Secondary:37A50, 60F05.

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  •   M. Abadi  and  A. Galves , Inequalities for the occurrence times of rare events in mixing processes, Markov Process. Related Fields, 7 (2001) , 97-112. 
      R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms Lecture Notes in Mathematics, 470. Springer-Verlag, Berlin, 2008.
      X. Bressaud  and  R. Zweimüller , Non exponential law of entrance times in asymptotically rare events for intermittent maps with infinite invariant measure, Ann. Henri Poincaré, 2 (2001) , 501-512.  doi: 10.1007/PL00001042.
      W. Feller, An Introduction to Probability Theory and its Application 2 2nd edition, Wiley, New york, 1971. doi: 10.2307/3029053.
      Y. Givarc'h  and  J. Hardy , Théorémes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov, Annales Inst. H. Poincaré(B), Probabilités et Statistiques, 24 (1988) , 73-98. 
      H. Hennion and L. Hervé, Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness Lecture Notes in Mathematics, 1766 Springer, Berlin, 2001. doi: 10.1007/b87874.
      M. Hirata , Poisson law for Axiom A diffeomorphisms, Ergodic Theory and Dynamical Systems, 13 (1993) , 533-556.  doi: 10.1017/S0143385700007513.
      S. V. Nagaev , Some limit theorems for stationary Markov chains, Theor. Probab. Appl., 2 (1957) , 378-406. 
      S. V. Nagaev , More exact statement of limit theores of homogeneous Markov chains, Theor. Probab. Appl., 6 (1961) , 62-81. 
      F. Péne  and  B. Saussol , Back to balls in billiards, Comm. Math. Phys., 293 (2010) , 837-866.  doi: 10.1007/s00220-009-0911-4.
      F. Péne  and  B. Saussol , Quantitative recurrence in two-dimensioinal extended processes, Ann. Inst. Henri Poincaré Probab. Stat., 45 (2009) , 1065-1084.  doi: 10.1214/08-AIHP195.
      F. Péne , B. Saussol  and  R. Zweimüller , Recurrence rates and hitting-time distributions for random walks on the line, The Annals of Probability, 41 (2013) , 619-635.  doi: 10.1214/11-AOP698.
      F. Péne , B. Saussol  and  R. Zweimüller , Return and hitting time limits for rare events of null-recurrent Markov maps, Ergod. Th. Dynam. Sys., 37 (2017) , 244-276.  doi: 10.1017/etds.2015.38.
      B. Saussol , An introduction to quantitative poincaré recurrence in dynamical systems, Reviews in Mathematical Physics, 21 (2009) , 949-979.  doi: 10.1142/S0129055X09003785.
      B. Saussol , Recurrence rate in rapidly mixing dynamical systems, Discrete and Continuous Dynamical Systems, 15 (2006) , 259-267.  doi: 10.3934/dcds.2006.15.259.
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