Asymptotics for return times of rank-one systems

Stochastics and Dynamics

Volumn 5, Issue 1, 2005, Pages 65-73

  Chaumoître, Vincent ^a   Kupsa, Michal ^b,c  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Asymptotics; Mixing; Rank one; Return times; Staircase transformation

Indexed keywords

EID: 33745229624     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493705001298     Document Type: Article

References (21)

1. T. M. Adams, Smorodinsky's conjecture on rank-one mixing, Proc. Amer. Math. Soc. 126 (1998) 739-744.
2. M. Abadi and A. Galves, Inequalities for the occurrence times of rare events in mixing processes, The state of art. Inhomogeneous random systems (Cergy-Pontoise, 2000), Markov Processes, Rel. Fields 7 (2001) 97-112.
3. H. Bruin, B. Saussol, S. Troubetzkoy and S. Vaienti, Return time statistics via inducing, Erg. Theory Dyn. Syst. 23 (2003) 991-1013.
4. R. V. Chacon, Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc. 22 (1969) 559-562.
5. Z. Coelho, Asymptotic laws for symbolic dynamical systems, in Proc. of the Conference held in Temuco, 1997, London Math. Soc. Lecture Note Ser., Vol. 279 (Cambridge Univ. Press, 2000), pp. 123-165.
6. Z. Coelho and P. Collet, Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle, Probab. Theory Rel. Fields 99 (1994) 237-250.
7. Z. Coelho and E. de Faria, Limit laws for entrance times for homeomorphisms of the circle, Israel J. Math. 93 (1996) 73-92.
8. P. Collet and A. Galves, Statistics of close visits to the indifferent fixed point of an interval map, J. Statist. Phys. 72 (1993) 459-478.
9. F. Durand and A. Maass, Limit laws of entrance times for low-complexity Cantor minimal systems, Nonlinearity 14 (2001) 683-700.
10. S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1997) 35-65.
11. N. A. Friedman, Introduction to Ergodic Theory (Van Nostrand, 1970).
12. N. A. Friedman, Mixing on sequences, Canad. J. Math. 35 (1983) 339-352.
13. M. Hirata, Poisson law for axiom a diffeomorphisms, Erg. Theory Dyn. Syst. 13 (1993) 533-556.
14. M. Hirata, Poisson law for the dynamical systems with the "self-mixing" conditions, in Dyn. Syst. Chaos, Vol. 1 (1994) (World Scientific, 1995), pp. 87-96.
15. N. Haydn, Y. Lacroix and S. Vaienti, Hitting and return times in ergodic dynamical systems, to appear.
16. M. Hirata, B. Saussol and S. Vaienti, Statistics of return times: A general framework and new applications, Comm. Math. Phys. 206 (1999) 33-55.
17. M. Kupsa and Y. Lacroix, Asymptotics for hitting times, to appear in Ann. Probab.
18. Y. Lacroix, Possible limit laws for entrance times of an ergodic aperiodic dynamical system, Israel J. Math. 132 (2002) 253-264.
19. B. Pitskel, Poisson limit law for Markov chains, Ergodic Theory Dyn. Syst. 11 (1991) 501-513.
20. B. Saussol, Etude statistique de systèmes dynamiques dilatants, PhD thesis, Toulon, France, 1998.
21. L. S. Young, Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188.