Isolating segments, fixed point index, and symbolic dynamics. III: Applications
type: Item
instance of: scholarly article
title: Isolating segments, fixed point index, and symbolic dynamics. III: Applications
zbMATH Open document ID: 1025.37013
author: Piotr Zgliczyński
author: Klaudiusz Wójcik
published in: Journal of Differential Equations
publication date: 2002-09-17T00:00:00Z
review text: The authors continue to study chaotic properties of the nonautonomous equation \[ z'=\bar{z}^n(1+e^{i\kappa t}|z|^2). \] The method of isolating segments is applied to establish the existence of an invariant set on which the Poincaré map has symbolic dynamics on \(n+2\) symbols. For Parts I and II see ibid. 161, 245-288 (2000; Zbl 0953.34034) and ibid. 172, 189-211 (2001; Zbl 0996.37020).
reviewed by: Sergei Yu. Pilyugin
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1801923
zbMATH Keywords: chaotic properties
zbMATH Keywords: nonautonomous equation
zbMATH Keywords: Poincaré map
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4099
OpenAlex ID: W2017397818
cites work: Q4180600
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cites work: Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations
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cites work: Isolating segments, fixed point index, and symbolic dynamics. II: Homoclinic solutions
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DOI: 10.1006/JDEQ.2001.4099
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description: scientific article; zbMATH DE number 1801923