Positive Lyapunov exponents in families of one dimensional dynamical systems. (English) Zbl 0787.58029

A generalization of Jakobson’s theorem [M. V. Jakobson, Commun. Math. Phys. 81, 39–88 (1981; Zbl 0497.58017)] concerning abundance of chaotic systems with absolutely continuous invariant measures in a typical family of one-dimensional dynamical systems is given. A new precise estimate for the density of the corresponding parameters is obtained.
Reviewer: H.D.Voulov (Sofia)


37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37E05 Dynamical systems involving maps of the interval
37A10 Dynamical systems involving one-parameter continuous families of measure-preserving transformations
28D05 Measure-preserving transformations


Zbl 0497.58017
Full Text: DOI EuDML


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