Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/55110
Type: Artigo
Title: Asymptotic angular stability in non-linear systems: rotation numbers and winding numbers
Title Alternative: 
Author: Mcsharry, Patrick E.
Ruffino, Paulo R.C.
Abstract: The asymptotic angular stability of a dynamical system may be quantified by its rotation number or its winding number. These two quantities are shown to result from different assumptions, made about the flow generating the Poincare map which results from the sequence of homeomorphisms in S-1. An ergodic theorem of existence a.s. of the rotation number for non-linear systems is given. The advantages and disadvantages of both the rotation and winding numbers are discussed. Numerical calculations of the distribution of rotation number and winding number arising from different initial conditions are presented for three different chaotic maps.
The asymptotic angular stability of a dynamical system may be quantified by its rotation number or its winding number. These two quantities are shown to result from different assumptions, made about the flow generating the Poincare map which results from the sequence of homeomorphisms in S-1. An ergodic theorem of existence a.s. of the rotation number for non-linear systems is given. The advantages and disadvantages of both the rotation and winding numbers are discussed. Numerical calculations of the distribution of rotation number and winding number arising from different initial conditions are presented for three different chaotic maps.
metadata.dc.description.abstractalternative: 
Subject: Estabilidade assintótica
Teoria ergódica
Métodos numéricos
Problemas de valor inicial
Country: Reino Unido
Editor: Taylor & Francis
Citation: Dynamical Systems-an International Journal. Taylor & Francis Ltd, v. 18, n. 3, n. 191, n. 200, 2003.
Rights: aberto
Identifier DOI: 10.1080/1468936031000155927
Address: https://www.tandfonline.com/toc/cdss20/18/3?nav=tocList
Date Issue: 2003
Appears in Collections:IMECC - Artigos e Outros Documentos

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