Dynamics of the complex standard family

DOI10.1006/jmaa.1998.6134zbMath0917.58037OpenAlexW2041082340MaRDI QIDQ1276320

Núria Fagella

Publication date: 5 August 1999

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1998.6134

zbMATH Keywords

iterationcircle homeomorphismFatou setArnold tongueHerman ring

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamical systems over complex numbers (37F99)

Related Items (15)

On a family of rational perturbations of the doubling map ⋮ Singular values and bounded Siegel disks ⋮ Analytic maps of parabolic and elliptic type with trivial centralisers ⋮ Dynamics of transcendental meromorphic functions (( )/( )) having rational Schwarzian derivatives ⋮ Dissipative feedback control and synchronization of Julia sets of the complex standard family ⋮ Siegel disks and periodic rays of entire functions ⋮ On the connectivity of the escaping set in the punctured plane ⋮ The escaping set of transcendental self-maps of the punctured plane ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ Slow escaping points of meromorphic functions ⋮ A separation theorem for entire transcendental maps ⋮ Function theory on annuli ⋮ Escaping Fatou components of transcendental self-maps of the punctured plane ⋮ Control and synchronization of Julia sets of the complex dissipative standard system ⋮ On the formulas of meromorphic functions with periodic Herman rings

Cites Work

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• Dynamical properties of some classes of entire functions
• Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals
• Local connectivity of the Julia set for geometrically finite rational maps
• Iteration of exponential functions
• Complex analytic dynamics on the Riemann sphere
• Dynamics of exp (z)
• Wandering domains for maps of the punctured plane
• Dynamics of entire functions near the essential singularity
• A finiteness theorem for a dynamical class of entire functions
• Rotation sets are closed
• Iteration of meromorphic functions
• The domains of normality of holomorphic self-maps of C^*

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