×

Non-hyperbolicity and invariant measures for unimodal maps. (English) Zbl 0717.58037

This paper gives a weak condition which guarantees the existence for a unimodal map f of an invariant probability measure which is absolutely continuous with respect to Lebesgue measure. The authors conjecture that this condition is actually equivalent to the existence of such a measure.
Reviewer: W.J.Satzer jun

MSC:

37A99 Ergodic theory
28D20 Entropy and other invariants
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] M. Benedicks and L.S. Young (to appear).
[2] A.M. Blokh and M.Yu. Lyubich , Measurable Dynamics of S-Unimodal Maps of the Internal , Preprint, 1989 . · Zbl 0790.58024
[3] P. Collet and J.-P. Eckmann , Positive Liapounov Exponents and Absolute Continuity for Maps of the Interval , Erg. Th. Dynam. Syst. , Vol. 3 , ( 13 - 46 ), 1983 . MR 743027 | Zbl 0532.28014 · Zbl 0532.28014 · doi:10.1017/S0143385700001802
[4] G. Keller , Exponents, Attractors, and Hopf Decompositions for Interval Maps , Preprint, 1988 . MR 1091423
[5] T. Nowicki and S.J. Van Strien , Absolutely Continuous Invariant Measures for C2 Maps Satisfying the Collet-Eckmann Conditions , Invent. Math. , Vol. 93 , 1988 , pp. 619 - 635 . MR 952285 | Zbl 0659.58034 · Zbl 0659.58034 · doi:10.1007/BF01410202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.