Complex universality
type: Item
instance of: scholarly article
title: Complex universality
zbMATH Open document ID: 0726.58034
DOI: 10.1007/BF01217804
author: Predrag Cvitanović
author: Jan Myrheim
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The authors generalize the results of Feigenbaum on the universal structure of period-doubling from real mappings to the complex case. They conjecture, that the fixed points of period n-tupling operators associated with infinite sequences of m/n period n-tuplings of complex mappings with quadratic critical points are universal and that the corresponding renormalization operators have a single unstable eigenvalue. The scaling numbers so obtained can be organized by Farey- trees and have well defined limits, which can be used to interprete the classical Feigenbaum number. The work mostly consists of numerical experiments and heuristic arguments and ends with notes on possible physical applications.
reviewed by: Clemens H. Cap
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 4199093
zbMATH Keywords: Mandelbrot set
zbMATH Keywords: complex iteration
zbMATH Keywords: period-doubling
zbMATH Keywords: Feigenbaum number
Wikidata QID: Q56969320
MaRDI profile type: Publication
cites work: Quantitative universality for a class of nonlinear transformations
cites work: The universal metric properties of nonlinear transformations
cites work: Universal scaling behaviour for iterated maps in the complex plane
cites work: Renormalization group analysis of quasi-periodicity in analytic maps
cites work: Q3908199
cites work: Q3696187
cites work: Roads to turbulence in dissipative dynamical systems
cites work: A two-dimensional mapping with a strange attractor
cites work: Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
cites work: Simple mathematical models with very complicated dynamics
cites work: Q4740120
cites work: Iteration of analytic functions
cites work: Scaling Laws for Mode Lockings in Circle Maps
full work available at URL: https://doi.org/10.1007/bf01217804
OpenAlex ID: W4251359091
description: scientific article; zbMATH DE number 4199093