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arXiv · 0907.0116

An entire transcendental family with a persistent Siegel disc

Ruben Berenguel·Nuria Fagella
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Abstract

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 $f_a$ with $a\in\mathbb{C}^*$ which includes the semi-standard map $λze^z$ at $a=1$, approaches the exponential map when $a\to0$ and a quadratic polynomial when $a\to\infty$. 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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Ruben Berenguel, Nuria Fagella. 2009-09-17. An entire transcendental family with a persistent Siegel disc. https://arxiv.org/abs/0907.0116

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