Asymptotic and essentially singular solutions of the Feigenbaum equation.

DOI10.1007/BF01014896zbMath1073.37520OpenAlexW1994183709MaRDI QIDQ1963674

Colin J. Thompson, J. B. McGuire

Publication date: 2 February 2000

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

Full work available at URL: https://doi.org/10.1007/bf01014896

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Dynamical systems involving maps of the interval (37E05)

Related Items (8)

The \(C^0\) solutions of the Feigenbaum-like functional equation ⋮ \(C^{\infty}\)-solutions for the second type of generalized Feigenbaum's functional equations ⋮ Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points ⋮ Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations ⋮ Physical meaning for Mandelbrot and Julia sets ⋮ Multi-modal-extended solutions of the Feigenbaum equation ⋮ Construction of convex solutions for the second type of Feigenbaum's functional equations ⋮ Dynamics and universality of unimodal mappings with infinite criticality

Cites Work

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• A shorter proof of the existence of the Feigenbaum fixed point
• Computer methods and Borel summability applied to Feigenbaum's equation
• New proofs of the existence of the Feigenbaum functions
• Universal properties of maps on an interval
• On the existence of Feigenbaum's fixed point
• Quantitative universality for a class of nonlinear transformations
• Asymptotic properties of sequences of iterates of nonlinear transformations
• Simple mathematical models with very complicated dynamics

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