Thick hyperbolic repelling invariant Cantor sets and wild attractors

Abstract

Let D be the set of such that f β is a symmetric tent map with finite critical orbit. For , by operating Denjoy-like surgery on f β , we constructed a C 1 unimodal map admitting a thick hyperbolic repelling invariant Cantor set which contains a wild attractor. The smoothness of is ensured by the effective estimation of the preimages of the critical point as well as the prescribed lengths of the inserted intervals. D is dense in , and can not be because the hyperbolic repelling invariant Cantor set of map has Lebesgue measure equal to zero.