The existence of absolutely continuous invariant measures is not a topological invariant for unimodal maps

Ergodic Theory and Dynamical Systems

Volumn 18, Issue 3, 1998, Pages 555-565

  Bruin, Henk ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

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EID: 0032395453     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385798100469     Document Type: Article

References (17)

1. A. Blokh and M. Lyubich. Measurable dynamics of S-unimodal maps of the interval. Ann. Scient. Ec. Norm. Sup. 24 (1991), 545-573.
2. H. Bruin. Invariant measures for interval maps. PhD Thesis, Delft, 1994.
3. H. Bruin. Combinatorics of the kneading map. Int. J. Bifur. Chaos 5(5) (1995), 1339-1349.
4. H. Bruin, G. Keller, T. Nowicki and S. van Strien. Wild Cantor attractors exist. Ann. Math. 143 (1996), 97-130.
5. J. Graczyk and G. Świa̧tek. Generic hyperbolicity in the logistic family. Ann. Math. 146 (1997), 1-52.
6. M. Herman. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publ. Math. IHES 49 (1979), 5-233.
7. F. Hofbauer and G. Keller. Some remarks on recent results about S-unimodal maps. Ann. Inst. Henri Poincaré, Physique théorique 53 (1990), 413-425.
8. M. Jakobson. Quasisymmetric conjugacies for some one-dimensional maps inducing expansion. Contemp. Math. 135 (1992), 203-211.
9. M. Jakobson and G. Świa̧tek. Metric properties of non-renormalizable S-unimodal maps II: Quasisymmetric conjugacy classes. Ergod. Th. & Dynam. Sys. 15 (1995), 871-938.
10. M. Lyubich and J. Milnor. The Fibonacci unimodal map. J. Amer. Math. Soc. 6 (1993), 425-457.
11. M. Martens. The existence of σ-finite measures, applications to 1-dimensional dynamics. Preprint, IMPA, Rio de Janeiro, 1991 and Stony Brook, 1992-1.
12. M. Misiurewicz. Absolutely continuous measures for certain maps of an interval. Publ. Math. IHES 53 (1981), 17-51.
13. W. de Melo and S. van Strien. One-Dimensional Dynamics. Springer, Berlin, Heidelberg, New York, 1993.
14. T. Nowicki and S. van Strien. Absolutely continuous measures under a summability condition. Invent. Math. 93 (1988), 619-635.
15. D. Sands and T. Nowicki. Quasisymmetric invariance of the Collet-Eckmann condition. Ergod. Th. & Dynam. Sys. 18 (1998), 703-715.
16. D. Sands. Topological conditions for positive Lyapunov exponent in unimodal maps. PhD Thesis, Cambridge, 1994.
17. J.-C. Yoccoz. Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition Diophantienne. Ann. Sci. Ec. Norm. Sup. 17 (1984), 333-361.