Universal scaling behaviour for iterated maps in the complex plane

DOI10.1007/BF01214743zbMath0523.30018OpenAlexW2015092163MaRDI QIDQ584568

Michael Nauenberg, Nicholas S. Manton

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01214743

zbMATH Keywords

Fibonacci numbersiterated maps

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)

Related Items (17)

Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number ⋮ Scaling properties of \({\mathbb{Z}}^{k-1}\) actions on the circle ⋮ Improved KAM estimates for the Siegel radius ⋮ Control of Julia sets of the complex Hénon system ⋮ Complex analytic dynamics on the Riemann sphere ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ On the universality of singular circle maps. ⋮ Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters ⋮ Unnamed Item ⋮ On the scaling ratios for Siegel disks ⋮ Transition to criticality in circle maps at the golden mean ⋮ Renormalization in the golden-mean semi-Siegel Hénon family: universality and non-rigidity ⋮ Self-similarity of Siegel disks and Hausdorff dimension of Julia sets ⋮ Boundaries of Siegel disks: Numerical studies of their dynamics and regularity ⋮ Renormalization group analysis of quasi-periodicity in analytic maps ⋮ Complex universality ⋮ Some comments on the non-self-dual Nahm equations

Cites Work

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• Invariant sets under iteration of rational functions
• On the nature of turbulence
• Roads to turbulence in dissipative dynamical systems
• Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory

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