Deterministic Chaos Theory: Basic Concepts

Detalhes bibliográficos
Autor(a) principal: Cattani,Mauro
Data de Publicação: 2017
Outros Autores: Caldas,Iberê Luiz, Souza,Silvio Luiz de, Iarosz,Kelly Cristiane
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000100409
Resumo: This article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.
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spelling Deterministic Chaos Theory: Basic Conceptschaos theorydifferential equationsPoincaré sectionsmappingLyapunov exponentThis article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.Sociedade Brasileira de Física2017-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000100409Revista Brasileira de Ensino de Física v.39 n.1 2017reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2016-0185info:eu-repo/semantics/openAccessCattani,MauroCaldas,Iberê LuizSouza,Silvio Luiz deIarosz,Kelly Cristianeeng2017-09-29T00:00:00Zoai:scielo:S1806-11172017000100409Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2017-09-29T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Deterministic Chaos Theory: Basic Concepts
title Deterministic Chaos Theory: Basic Concepts
spellingShingle Deterministic Chaos Theory: Basic Concepts
Cattani,Mauro
chaos theory
differential equations
Poincaré sections
mapping
Lyapunov exponent
title_short Deterministic Chaos Theory: Basic Concepts
title_full Deterministic Chaos Theory: Basic Concepts
title_fullStr Deterministic Chaos Theory: Basic Concepts
title_full_unstemmed Deterministic Chaos Theory: Basic Concepts
title_sort Deterministic Chaos Theory: Basic Concepts
author Cattani,Mauro
author_facet Cattani,Mauro
Caldas,Iberê Luiz
Souza,Silvio Luiz de
Iarosz,Kelly Cristiane
author_role author
author2 Caldas,Iberê Luiz
Souza,Silvio Luiz de
Iarosz,Kelly Cristiane
author2_role author
author
author
dc.contributor.author.fl_str_mv Cattani,Mauro
Caldas,Iberê Luiz
Souza,Silvio Luiz de
Iarosz,Kelly Cristiane
dc.subject.por.fl_str_mv chaos theory
differential equations
Poincaré sections
mapping
Lyapunov exponent
topic chaos theory
differential equations
Poincaré sections
mapping
Lyapunov exponent
description This article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.
publishDate 2017
dc.date.none.fl_str_mv 2017-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000100409
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000100409
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2016-0185
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.39 n.1 2017
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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