Abstract
Consider the parameter space Pλ⊂C2 of complex Hénon mapsHc,a(x,y)=(x2+c+ay,ax),a≠0, which have a semi-parabolic fixed point with one eigenvalue λ=e2πip/q. In this paper we provide a complete topological description of the Julia set and forward Julia set within a family of semi-parabolic Hénon maps, i.e. those Hénon maps from the curve Pλ which are perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier λ. We prove that there is an open disk of parameters in Pλ for which the semi-parabolic Hénon map has connected Julia set J and is structurally stable on J and J+. The forward Julia set J+ has a nice local description: inside a certain bidisk it is a trivial fiber bundle over Jp, the Julia set of the polynomial p, with fibers biholomorphic to a disk. The Julia set J is homeomorphic to the quotient of a solenoid by an equivalence relation and J=J⁎, the closure of the saddle periodic points.
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