On the Convergence of Hyperbolic Components in Families of Finite Type
نویسنده
چکیده
We study approximations of analytic families G(;) of entire functions by analytic families F n (;), for example polynomials, where 2 C. In order to control the dynamics of these functions the families are assumed to be of constant nite type. In this setting we prove the convergence of the hyperbolic components as kernels in the sense of Carath eodory, which is a stronger notion than the usual pointwise convergence. We give an example that in general the hyperbolic components do not converge in the Hausdorr metric as the Julia sets do.
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