Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations

DOI10.1142/S0218127498000206zbMath0932.37003MaRDI QIDQ4936198

George Szekeres, Tony W. Dixon, Keith M. Briggs

Publication date: 24 January 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

divergent seriessingular solutionAbel functional equationscircle mapsSchrödinger functional equations

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Iteration theory, iterative and composite equations (39B12) Symbolic dynamics (37B10)

Related Items (17)

Metric universalities and systems of renormalization group equations for bimodal maps ⋮ FORMAL SOLUTIONS OF THE CVITANOVIC–FEIGENBAUM EQUATION ⋮ Single-valley-extended solutions with platforms of FKS equation ⋮ A new type of period-doubling scaling behavior in two-dimensional area-preserving map ⋮ On the universality of singular circle maps. ⋮ Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points ⋮ Multi-modal-extended solutions of FKS equation ⋮ Scaling in a Map of the Two-Torus ⋮ Multiparameter critical situations, universality and scaling in two-dimensional period-doubling maps ⋮ Statistical analysis of the first digits of the binary expansion of Feigenbaum constants \(\alpha\) and \(\delta\) ⋮ Single-valley solutions of the second type of FKS equation ⋮ Differentiable solutions of the Feigenbaum-Kadanoff-Shenker equation ⋮ Transition to criticality in circle maps at the golden mean ⋮ Regularity of Conjugacies between Critical Circle Maps: An Experimental Study ⋮ Multi-modal-extended solutions of the Feigenbaum equation ⋮ Dynamics and universality of unimodal mappings with infinite criticality ⋮ Rigorous computer-assisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4

Cites Work

• Bounds on the unstable eigenvalue for period doubling
• On Feigenbaum's functional equation gg(lambdax)+lambdag(x)=0
• The universal metric properties of nonlinear transformations
• Functional equations for circle homeomorphisms with golden ratio rotation number
• On the existence of fixed points of the composition operator for circle maps
• New proofs of the existence of the Feigenbaum functions
• Period doubling in maps with a maximum of order
• Quantitative universality for a class of nonlinear transformations
• Asymptotic properties of sequences of iterates of nonlinear transformations
• Asymptotic and essentially singular solutions of the Feigenbaum equation.
• On the universality of singular circle maps.
• An improvement of Watson’s theorem on Borel summability
• Relations between universal scaling constants for the circle map near the golden mean

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