An entire transcendental family with a persistent Siegel disc

DOI10.1080/10236190903251738zbMath1198.30026arXiv0907.0116OpenAlexW2078306927MaRDI QIDQ3570128

Ruben Berenguel, Núria Fagella

Publication date: 24 June 2010

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0116

zbMATH Keywords

dynamical systemsSiegel discHadamard's factorization theoremtranscendental mapsBrjuno number

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50)

Related Items (4)

Convergence of rays with rational argument in hyperbolic components—an illustration in transcendental dynamics ⋮ Quadratic rational maps with a 2-cycle of Siegel disks ⋮ Stable components in the parameter plane of transcendental functions of finite type ⋮ Siegel disks of the tangent family

Cites Work

• Are there critical points on the boundaries of singular domains?
• Fixed points and circle maps
• Dynamics of cubic Siegel polynomials
• Iteration of analytic functions
• Siegel discs, Herman rings and the Arnold family
• Singularities in the boundaries of local Siegel disks
• Siegel disks and periodic rays of entire functions
• HAIRS FOR THE COMPLEX EXPONENTIAL FAMILY
• A finiteness theorem for a dynamical class of entire functions
• On a theorem of Fatou
• LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY
• Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery
• ON A QUESTION OF HERMAN, BAKER AND RIPPON CONCERNING SIEGEL DISKS
• Quasiconformal Surgery in Holomorphic Dynamics

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