On basin boundaries
type: Item
instance of: scholarly article
title: On basin boundaries
zbMATH Open document ID: 0929.37018
DOI: 10.1016/S0096-3003(97)10184-9
author: T. Narayaninsamy
published in: Applied Mathematics and Computation
publication date: 2000-02-02T00:00:00Z
review text: The author considers the map \(T= (T_1,T_2): \mathbb{R}^2\to \mathbb{R}^2\) which is defined by \[ (x,y)\mapsto (T_1, T_2) (x,y):= (x^2- y^2+ \lambda+ \varepsilon f_1(x,y), \;2xy+ \varepsilon f_2(x,y)), \tag{1} \] where \(\lambda\in ]-\frac 34, \frac 14[\), \(\varepsilon\in \mathbb{R}\), \(f= (f_1,f_2)\) is a differentiable map, such that when \(\varepsilon\neq 0\), \(T\) is a non-analytic map. Note that the map \(T\) can be considered as a perturbation of the polynomial complex \(z\mapsto z^2+ \lambda\). The purpose of this note is to study a class of basin boundaries which is generated by (1). The author shows that an efficient characterization of a given element of this class can be constructed with segments of differentiable curves.
Mathematics Subject Classification ID: 37G35
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 1311103
zbMATH Keywords: non-analytic map
zbMATH Keywords: polynomial complex
zbMATH Keywords: basin boundary
zbMATH Keywords: differentiable curves
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Fractal basin boundaries
cites work: Q4842394
cites work: Q3885588
cites work: ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES
cites work: Q3314128
full work available at URL: s0096-3003(97)10184-9
OpenAlex ID: W2007228459
description: scientific article; zbMATH DE number 1311103