Renormalization in the Hénon family. I: Universality but non-rigidity

DOI10.1007/s10955-005-8668-4zbMath1098.37039arXivmath/0508477OpenAlexW2126230451WikidataQ57740108 ScholiaQ57740108MaRDI QIDQ2492844

Marco Martens, André de Carvalho, Mikhail Lyubich

Publication date: 14 June 2006

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

Full work available at URL: https://arxiv.org/abs/math/0508477

zbMATH Keywords

Hénon-like mapsHénon renormalization operatorperiod-doubling renormalization

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20)

Related Items (37)

Renormalization in the golden-mean semi-Siegel Hénon family: non-quasisymmetry ⋮ Asymptotic scaling and universality for skew products with factors in SL(2,) ⋮ The Lorenz Renormalization Conjecture ⋮ Dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\): combinatorial and topological aspects ⋮ On parameter loci of the Hénon family ⋮ On the invariant Cantor sets of period doubling type of infinitely renormalizable area-preserving maps ⋮ Infinitely many moduli of stability at the dissipative boundary of chaos ⋮ Dynamics of deformed Hénon-like map ⋮ Renormalization of almost commuting pairs ⋮ A structure theorem for semi-parabolic Hénon maps ⋮ Scenarios for the creation of hyperchaotic attractors in 3D maps ⋮ Polynomial entropy of Morse-Smale diffeomorphisms on surfaces ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ Renormalization in the Hénon family. II: The heteroclinic web ⋮ Newhouse Laminations of polynomials on ℂ2 ⋮ The Boundaries of Golden-Mean Siegel Disks in the Complex Quadratic Hénon Family Are Not Smooth ⋮ Unnamed Item ⋮ PERIOD DOUBLING RENORMALIZATION FOR AREA-PRESERVING MAPS AND MILD COMPUTER ASSISTANCE IN CONTRACTION MAPPING PRINCIPLE ⋮ The rigidity conjecture ⋮ A numerical study of infinitely renormalizable area-preserving maps ⋮ Period-doubling cascades galore ⋮ Probabilistic universality in two-dimensional dynamics ⋮ Renormalization and Siegel disks for complex Hénon maps ⋮ Fractals as objects with nontrivial structures at all scales ⋮ Classification of invariant Fatou components for dissipative Hénon maps ⋮ Rigidity for infinitely renormalizable area-preserving maps ⋮ Nonexistence of wandering domains for strongly dissipative infinitely renormalizable Hénon maps at the boundary of chaos ⋮ Renormalization of symmetric bimodal maps with low smoothness ⋮ Structural instability of semi-Siegel Hénon maps ⋮ Merger of a Hénon-like attractor with a Hénon-like repeller in a model of vortex dynamics ⋮ Renormalization in the golden-mean semi-Siegel Hénon family: universality and non-rigidity ⋮ Hénon-like maps with arbitrary stationary combinatorics ⋮ Lebesgue measure of Feigenbaum Julia sets ⋮ Topological horseshoes for surface homeomorphisms ⋮ HÉNON MAP: SIMPLE SINKS GAINING COEXISTENCE AS b → 1 ⋮ Invariant manifolds for non-differentiable operators ⋮ Spectral properties of renormalization for area-preserving maps

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