Dimension of Markov towers for non uniformly expanding one-dimensional systems

Discrete and Continuous Dynamical Systems

Volumn 9, Issue 6, 2003, Pages 1447-1464

  Sánchez Salas, Fernando J ^a  

^a FACULTAD DE CIENCIAS VETERINARIAS   (Venezuela)

Author keywords

Absolutely continuous invariant measures; Entropy; Hausdorff dimension; Induced Markov transformations; Markov towers; Non uniformly expanding systems; Pesin entropy formula; Positive Lyapunov exponents

Indexed keywords

EID: 0346283253     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2003.9.1447     Document Type: Article

References (18)

1. José F. Alves (2002) : Non-uniformly expanding dynamics: stability from a probabilistic viewpoint, Discrete and Continuous Dynamical Systems, 8 (2), 363-376
2. Alves, J.F. - Luzzatto, S. - Pinheiro, V. (2002) : Markov structures for non uniformly expanding maps on compact manifolds in arbitrary dimension, C.R. Acad. Sci. Paris
3. Bruin. H. (1995) : Induced maps. Markov extensions and invariant measures in one-dimensional dynamics. Commun. Math. Phys. 168, 571-580
4. De Melo, W. - Van Strien (1993) : One Dimensional Dynamics. Springer-Verlag
5. Falconer, J.: Fractal Geometry. Cambridge University Press
6. Hofbauer, F. (1995) : Local dimension for piecewise monotonic maps on the interval. Erg. Th. and Dynam. Sys. 15, 1119-1142
7. Katok, A. - Mendoza, L. (1995) : Dynamical systems with non-uniformly hyperbolic behavior. Supplement to Introduction to the Modern Theory of Dynamical Systems, by Katok, A. and Hasselblat, B. Encyclopedia of Math. and its Applications 54. Cambridge University Press
8. Keller, G. (1989) : Lifting measures to Markov extension. Monath. Math. 108, 183 - 200
9. Ledrappier, F. (1981) : Some properties of absolutely continuous invariant measures. Erg. Th. and Dyn. Sys. 1, 77-93
10. Ledrappier, F. - Misiurewicz, M. (1985) : Dimension of invariant measures for maps with entropy zero. Erg. Th. and Dyn, Sys. 5, 595-610
11. Ledrappier, F. - Strelcyn, J.M. (1982) : Proof of the estimation from below in Pesin's entropy formula. Erg. Th. and Dyn. Sys. 2 203-219
12. Ledrappier, F. - L.-S. Young (1985) : Entropy of diffeomorphisms. Ann. of Math. 122, 509574
13. Mendoza, L. (1988) : Ergodic attractors for diffeomorphisms of surfaces. Journal of the London Math. Soc. 37 (2), 362-374
14. Pesin, Ya. (1997) : Dimension Theory and Dynamical Systems. Chicago Lectures on Mathematics
15. Petersen, K. (1983) : Ergodic Theory. Cambridge University Press
16. Ruelle, D. (1979) : Ergodic theory of differentiate dynamical systems. Publications Math. HIES 50, 27-58
17. Sánchez-Salas (2002) : Ergodic attractors as limits of hyperbolic horseshoes. Erg. Th. and Dyn. Sys. 22, 571-589
18. Young, L.-S. (1998): Statistical properties of dynamical systems with some hyperbolicity. Annals of Math. 147, 585-650