Computable Conditions for the Occurrence of Non-uniform Hyperbolicity in Families of One-dimensional Maps
نویسندگان
چکیده
Abstract. We formulate and prove a Jakobson-Benedicks-Carleson type theorem on the occurence of nonuniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on computable starting conditions and providing explicit, computable, lower bounds for the measure of the set of selected parameters. As a first application of our results we show that the set of parameters corresponding to maps in the quadratic family fa(x) = x 2 − a which have an absolutely continuous invariant probability measure is at least 10.
منابع مشابه
Computable Condition for the Occurrence of Non-uniform Hyperbolicity in Families of One-dimensional Maps
can display a wide variety of dynamics which are closely intertwined. Graczyk-Świa̧teck proved that the set of regular parameters (corresponding to a hyperbolic periodic attractor) is open dense. Lyubich [8] proved that almost every parameter is either regular or stochastic (corresponding to an absolutely continuous invariant measure, acim for short). The second possibility in this dichotomy is ...
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