An entire transcendental family with a persistent Siegel disc
Berenguel, Rubén (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)

Date:	2010
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 disk. After normalization this is a one parameter family fa with a ∈ C which includes the semistandard 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 disk in terms of the parameter.
Grants:	Ministerio de Ciencia e Innovación MTM2006-05849 Ministerio de Ciencia e Innovación MTM2008-01486 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-01028
Note:	Altres ajuts: Consolider and European funds MCRTN-CT-2006-035651
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Siegel disc ; Transcendental maps ; Riemann ; Dynamical systems
Published in:	Journal of Difference Equations and Applications, Vol. 16, Issue 5-6 (May 2010) , p. 523-553, ISSN 1563-5120

DOI: 10.1080/10236190903251738

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