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Global weak solutions to the Camassa-Holm equation
Transversal families of hyperbolic skew-products
1. | Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O Box 1-764, RO 014-700, Bucharest |
2. | Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430 |
We introduce and employ probability measures (constructed from equilibrium measures on the natural extension), which are supported on the fibers of the skew product. A stronger condition, that of Uniform Transversality is then considered in order to obtain a general formula for Hausdorff dimension of fibers for all base points and almost all parameters.
In the end we study a large class of examples of transversal hyperbolic families which locally depend linearly on the parameters, and also another class of examples related to complex dynamics.
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