Complex a priori bounds revisited.

DOI10.5802/afst.1061zbMath1070.37029OpenAlexW1973075338MaRDI QIDQ1890437

Michael Yampolsky

Publication date: 3 January 2005

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2003_6_12_4_533_0

zbMATH Keywords

rigiditynormalizationscomplex a priori boundsparabolic Julia setsperturbations of parabolic mapsreal quadratic polynomials

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Universality and renormalization of dynamical systems (37E20) Renormalization of holomorphic dynamical systems (37F25)

Related Items (2)

Real quadratic Julia sets can have arbitrarily high complexity ⋮ Computational intractability of attractors in the real quadratic family

Cites Work

• The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
• Local connectivity of the Julia set of real polynomials
• Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture
• Dynamics of quadratic polynomials: complex bounds for real maps
• Dynamics of quadratic polynomials. I, II
• Combinatorics, geometry and attractors of quasi-quadratic maps
• Almost every real quadratic map is either regular or stochastic.
• The set of maps \(F_{a,b}:x\mapsto x+a+{b\over 2\pi}\sin(2\pi x)\) with any given rotation interval is contractible
• Complex Dynamics and Renormalization (AM-135)
• Renormalization and 3-Manifolds Which Fiber over the Circle
• Parabolic limits of renormalization
• The attractor of renormalization and rigidity of towers of critical circle maps
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