An entire transcendental family with a persistent Siegel disc
نویسندگان
چکیده
We study the class of entire transcendental maps of finite order with one critical point and one asymptotic value, which has exactly one finite pre-image, and having a persistent Siegel disc. After normalisation this is a one parameter family fa with a ∈ C ∗ which includes the semi-standard map λzez at a = 1, approaches the exponential map when a → 0 and a quadratic polynomial when a → ∞. We investigate the stable components of the parameter plane (capture components and semi-hyperbolic components) and also some topological properties of the Siegel disc in terms of the parameter.
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