An entire transcendental family with a persistent Siegel disc

作者：Berenguel Ruben; Fagella Nuria^*

来源：Journal of Difference Equations and Applications, 2010, 16(5-6): 523-553.

DOI：10.1080/10236190903251738

• Siegel disc
• transcendental maps
• Riemann
• dynamical systems

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 normalization, this is a one parameter family f(a) with a is an element of C* which includes the semi-standard map lambda ze(z) at a = 1, approaches the exponential map when a -> 0 and a quadratic polynomial when a -> infinity. 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.

• 出版日期2010