## 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

### Keywords:

unimodal map; invariant probability measure
Full Text:

### 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 [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
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