Computer assisted proof of chaotic dynamics in the Rössler map
type: Item
instance of: scholarly article
title: Computer assisted proof of chaotic dynamics in the Rössler map
zbMATH Open document ID: 1002.65137
DOI: 10.12775/TMNA.2001.030
author: Daniel Wilczak
published in: Topological Methods in Nonlinear Analysis
publication date: 2002-12-20T00:00:00Z
review text: This paper is concerned with a two--dimensional discrete dynamical system induced by the so called Rössler map \( f: {\mathbb R}^2 \to {\mathbb R}^2 \) given by \( f(x,y)= ( 3.8 x (1-x) - 0.1 y, 0.2 ( y - 1.2) ( 1 - 1.9 x))\). The main result is a proof of the existence of symbolic dynamics for the third iterate which combines topological results based on the fixed point index with some inclusions that have been checked by using numerical computations.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65P20
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37M99
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1751368
zbMATH Keywords: discrete dynamical system
zbMATH Keywords: fixed point index
zbMATH Keywords: Rössler map
zbMATH Keywords: computer assisted proofs
zbMATH Keywords: symbolic dynamics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1751368