Families of Baker Domains Ii
نویسنده
چکیده
Let f be a transcendental meromorphic function and U be an invariant Baker domain of f . We use estimates for the hyperbolic metric to show that there is a relationship between the size of U and the proximity of f in U to the identity function, and illustrate this by discussing how the dynamics of transcendental entire functions of the following form vary with the parameter a: f(z) = az + bzke−z(1 + o(1)) as <(z)→∞, where k ∈N, a ≥ 1 and b > 0.
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