Existence of generic homoclinic tangencies for Hénon mappings

DOI10.1007/BF02921300zbMath0780.58031OpenAlexW2041473220MaRDI QIDQ1203498

John-Erik Fornaess, Estela Ana Gavosto

Publication date: 10 February 1993

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921300

zbMATH Keywords

iterationstrange attractorstable manifoldunstable manifoldpolynomial map

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (5)

How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency ⋮ Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds ⋮ Tangencies for Real and Complex Hénon Maps: An Analytic Method ⋮ Attracting basins in \({\mathbb{P}}^2\) ⋮ The parameterization method for invariant manifolds. III: Overview and applications

Cites Work

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• The dynamics of the Hénon map
• Bifurcation to infinitely many sinks
• Stable and unstable manifolds of the Henon mapping
• A two-dimensional mapping with a strange attractor
• Existence of a homoclinic point for the Henon map
• Complex Hénon mappings in \({\mathbb{C}}^ 2\) and Fatou-Bieberbach domains
• Abundance of strange attractors
• Hénon mappings in the complex domain. I: The global topology of dynamical space
• Diffeomorphisms with infinitely many sinks
• Polynomial diffeomorphisms of \({\mathbb C}^2\): Currents, equilibrium measure and hyperbolicity
• Complex analytic dynamics on the Riemann sphere
• A computer-assisted proof of the Feigenbaum conjectures

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