Chaotic behavior in the Helleman mapping
type: Item
instance of: scholarly article
title: Chaotic behavior in the Helleman mapping
zbMATH Open document ID: 0634.58018
DOI: 10.1007/BF02458262
author: Baolong Cheng
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1987-01-01T00:00:00Z
review text: The purpose of this paper is to obtain a sufficient condition, satisfied by a pair of parameters, for which a two-dimensional real quadratic diffeomorphism has the qualitative properties of the Smale horseshoe. This diffeomorphism is called here ``Helleman mapping'', which is only a variant of the known Hénon map. In the case of the Hénon map, the result of the author can be compared with those of other authors, not quoted [see, e.g., \textit{R. Devaney} and \textit{Z. Nitecki}, Commun. Math. Phys. 67, 137-146 (1979; Zbl 0414.58028); \textit{H. El Hamouly} and the reviewer, C. R. Acad. Sci., Paris, Sér. I 293, 525-528 (1981; Zbl 0482.58025); \textit{P. Holmes} and \textit{D. Whitley}, Phil. Trans. R. Soc. Lond., A 311, 43-102 (1984; Zbl 0556.58023)].
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 57R35
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 4032655
zbMATH Keywords: diffeomorphism
zbMATH Keywords: recurrence
zbMATH Keywords: iteration
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: Smale horseshoe
zbMATH Keywords: Hénon map
reviewed by: Christian Mira
MaRDI profile type: Publication
cites work: Stable and Random Motions in Dynamical Systems
cites work: A two-dimensional mapping with a strange attractor
cites work: Characteristic exponents and strange attractors
full work available at URL: https://doi.org/10.1007/bf02458262
OpenAlex ID: W2072062621
description: scientific article; zbMATH DE number 4032655