Geometry of the Feigenbaum map

DOI10.1090/S1088-4173-99-00031-4zbMath0956.37032arXivmath/9711216MaRDI QIDQ4485781

Xavier Buff

Publication date: 18 June 2000

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9711216

zbMATH Keywords

basin of attractionJulia setFeigenbaum fixed point

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Renormalization of holomorphic dynamical systems (37F25)

Related Items (5)

On the Lebesgue measure of the Feigenbaum Julia set ⋮ Poly-time computability of the Feigenbaum Julia set ⋮ On the topology of the inverse limit of a branched covering over a Riemann surface ⋮ Renormalization in the Hénon family. I: Universality but non-rigidity ⋮ On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization

Cites Work

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• The universal metric properties of nonlinear transformations
• A complete proof of the Feigenbaum conjectures
• Quantitative universality for a class of nonlinear transformations
• Fixed points of composition operators. II
• On the dynamics of polynomial-like mappings
• A computer-assisted proof of the Feigenbaum conjectures
• Renormalization and 3-Manifolds Which Fiber over the Circle

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