Thick hyperbolic repelling invariant Cantor sets and wild attractors

摘要

Let D be the set of beta is an element of (1, 2] such that f(beta) is a symmetric tent map with finite critical orbit. For beta is an element of D, by operating Denjoy-like surgery on f(beta), we constructed a C-1 unimodal map g(beta) admitting a thick hyperbolic repelling invariant Cantor set which contains a wild attractor. The smoothness of (g) over bar (beta) 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 (1, 2], and (g) over bar (beta) can not be C1+alpha because the hyperbolic repelling invariant Cantor set of C1+alpha map has Lebesgue measure equal to zero.

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