Existence of generic homoclinic tangencies for Hénon mappings
type: Item
instance of: scholarly article
title: Existence of generic homoclinic tangencies for Hénon mappings
zbMATH Open document ID: 0780.58031
DOI: 10.1007/BF02921300
published in: The Journal of Geometric Analysis
publication date: 1993-02-10T00:00:00Z
review text: A computer-assisted rigorous proof is given of the following Theorem: The map \(H_{a,b}:\mathbb{R}^ 2\to\mathbb{R}^ 2\), \(H_{ab}(x,y)=(1-ax^ 2+by,x)\), has a generic homoclinic tangency for the one-parameter family \(H_{a,b}\) for some parameter \(a=1.3924198079\ldots\) and any fixed \(b\) close to 0.3. This parameter value for \(a\) is close to Hénon's original value of \(a=1.4\). The proof relies on complexification and estimates of the power series expansions of the stable and unstable manifolds.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 118432
zbMATH Keywords: polynomial map
zbMATH Keywords: strange attractor
zbMATH Keywords: stable manifold
zbMATH Keywords: unstable manifold
zbMATH Keywords: iteration
author: J. E. Fornæss
author: Estela Ana Gavosto
reviewed by: Dieter Erle
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921300
OpenAlex ID: W2041473220
description: scientific article; zbMATH DE number 118432