Extreme values for Benedicks-Carleson quadratic maps

Ergodic Theory and Dynamical Systems

Volumn 28, Issue 4, 2008, Pages 1117-1133

  Freitas, Ana Cristina Moreira ^a   Freitas, Jorge Milhazes ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47249134179     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385707000624     Document Type: Article

References (20)

1. V. Balakrishnan, C. Nicolis and G. Nicolis. Extreme value distributions in chaotic dynamics. J. Stat. Phys. 80(1-2) (1995), 307-336.
2. 2 on (-1, 1). Ann. Math. 122 (1985), 1-25.
3. M. Benedicks and L. Carleson. The dynamics of the Hénon map. Ann. Math. 133 (1991), 73-169.
4. M. Benedicks and L. S. Young. Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps. Ergod. Th. & Dynam. Sys. 12 (1992), 13-27.
5. P. Collet and J. P. Eckmann. Positive Lyapunov exponents and absolute continuity for maps of the interval. Ergod. Th. & Dynam. Sys. 3 (1983), 13-46.
6. P. Collet. Statistics of closest return for some non-uniformly hyperbolic systems. Ergod. Th. & Dynam. Sys. 21(2) (2001), 401-420.
7. J. M. Freitas. Continuity of SRB measure and entropy for Benedicks-Carleson quadratic maps. Nonlinearity 18 (2005), 831-854.
8. J. M. Freitas. Statistical stability for chaotic dynamical systems. PhD Thesis. Universidade do Porto, 2006, http://www.fc.up.pt/pessoas/ jmfreita/homeweb/publications.htm.
9. A. C. M. Freitas and J. M. Freitas. On the link between dependence and independence in extreme value theory for dynamical systems. Statist. Probab. Lett. to appear.
10. G. Haiman. Extreme values of the tent map process. Statist. Probab. Lett. 65(4) (2003), 451-456.
11. M. Jakobson. Absolutely continuous invariant measures for one parameter families of one-dimensional maps. Comm. Math. Phys. 81 (1981), 39-88.
12. G. Keller. Exponential weak Bernoulli mixing for Collet-Eckmann maps. Israel J. Math, 86 (1994), 301-310.
13. G. Keller and T. Nowicki. Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps. Comm. Math. Phys. 149 (1992), 31-69.
14. J. F. C. Kingman and S. J. Taylor. Introduction to Measure and Probability. Cambridge University Press, Cambridge, 1966.
15. G. Lindgren, M. R. Leadbetter and H. Rootzén. Extremes and Related Properties of Stationary Sequences and Processes (Springer Series in Statistics, XII). Springer, New York, 1983.
16. W. de Melo and S. van Strien. One-Dimensional Dynamics. Springer, Berlin, 1993.
17. F. J. Moreira. Chaotic dynamics of quadratic maps, Informes de Matemática, IMPA, Série A, 092/93, 1993, http://www.fc.up.pt/cmup/ fsmoreir/downloads/BC.pdf.
18. T. Nowicki. Symmetric S-unimodal mappings and positive Liapunov exponents. Ergod Th. & Dynam. Sys. 5 (1985), 611-616.
19. M. Rychlik. Another proof of Jakobson's theorem and related results. Ergod. Th. & Dynam. Sys. 8(1) (1988), 93-109.
20. L. S. Young. Decay of correlations for certain quadratic maps. Comm. Math. Phys. 146 (1992), 123-138.