Transition to criticality in circle maps at the golden mean

DOI10.1063/1.532607zbMath0927.37022OpenAlexW2085814488MaRDI QIDQ4701533

Tony W. Dixon, B. G. Kenny

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532607

zbMATH Keywords

functional equationssubcritical solutiongolden mean eigenvalue equationsone-dimensional circle mapquasiperiodic route to chaos

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Universality and renormalization of dynamical systems (37E20)

Related Items

Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points

Cites Work

• Universal scaling behaviour for iterated maps in the complex plane
• Renormalization group analysis of quasi-periodicity in analytic maps
• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
• Universal properties of maps of the circle with \(\epsilon\)-singularities
• The universal metric properties of nonlinear transformations
• Universal properties of maps on an interval
• Quantitative universality for a class of nonlinear transformations
• Fractal dimensions and homeomorphic conjugacies.
• On the universality of singular circle maps.
• Relations between universal scaling constants for the circle map near the golden mean
• Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations