Sur certaines zones absorbantes et zones chaotiques d'un endomorphisme bidimensionnel. (On certain absorptive areas and chaotic areas of a two- dimensional endomorphism)
type: Item
instance of: scholarly article
title: Sur certaines zones absorbantes et zones chaotiques d'un endomorphisme bidimensionnel. (On certain absorptive areas and chaotic areas of a two- dimensional endomorphism)
zbMATH Open document ID: 0625.58006
DOI: 10.1016/0020-7462(86)90029-6
author: Alexandre Barugola
published in: International Journal of Non-Linear Mechanics
publication date: 1986-01-01T00:00:00Z
review text: Let T be an \(R^ 2\)-endomorphism (x;y)\(\to (f(x,y,\lambda);g(x,y,\lambda))\), f, g being continuous and smooth functions of the real variables x, y and the real parameter \(\lambda\). The endomorphism T is supposed to be of the type with vanishing Jacobian on a curve of the (x,y) plane, the first rank consequent of which is called the first rank critical curve. Papers quoted in the bibliography have shown that critical curves of various ranks play a fundamental role for the determination of chaotic properties of T. In particular, these properties are related to the existence of absorptive areas, and chaotic areas, the boundaries of which are segments of such critical curves. This paper gives a practical method for the construction of these boundaries from three propositions proved for a well defined class of \(R^ 2\)- endomorphisms.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 57R35
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 4015743
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: \(R^ 2\)-endomorphism
zbMATH Keywords: iteration
zbMATH Keywords: recurrence
zbMATH Keywords: critical curve
zbMATH Keywords: absorptive areas
zbMATH Keywords: chaotic areas
reviewed by: Christian Mira
MaRDI profile type: Publication
full work available at URL: 0020-7462(86)90029-6
OpenAlex ID: W2078108654
description: scientific article; zbMATH DE number 4015743