Renormalization group analysis of quasi-periodicity in analytic maps

DOI10.1007/BF01206316zbMath0535.58037MaRDI QIDQ791221

Michael Widom

Publication date: 1983

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

zbMATH Keywords

chaosquasiperiodicitySiegel domaincomplex mapping

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Celestial mechanics (70F15) Renormalization of holomorphic dynamical systems (37F25)

Related Items (15)

An iterated implicit complex map ⋮ Parabolic bifurcation loci in the spaces of rational functions ⋮ 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 ⋮ 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 ⋮ Complex universality

Cites Work

• Universal scaling behaviour for iterated maps in the complex plane
• Analyticity properties of the Feigenbaum function
• Critical Behavior of a KAM surface. I: Empirical results
• Quantitative universality for a class of nonlinear transformations
• Invariant sets under iteration of rational functions
• Iteration of analytic functions
• Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory
• Unnamed Item
• Unnamed Item

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