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Master's Dissertation
DOI
10.11606/D.43.1984.tde-28092012-155809
Document
Author
Full name
Cesar Rogerio de Oliveira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1984
Supervisor
Committee
Malta, Coraci Pereira (President)
Coutinho, Francisco Antonio Bezerra
Oliveira, Mario Jose de
Title in Portuguese
BIFURCACOES SUCESSIVAS EM SISTEMAS DE DIMENSAO INFINITA
Keywords in Portuguese
MECÂNICA ESTATÍSTICA
Abstract in Portuguese
Com base em exemplos, nos fundamentos da Mecânica estatística e na teoria ergódiga, é dada uma definição de atrator como uma medida invariante. Vários resultados que corroboram esta definição são demostrados. Caos é relacionado à presença de um atrator com entropia métrica maior que zero. O papel dos expoentes de Lyapunov é analisado e é provado que um atrator caótica possui expoentes de Lyapunov positivos em quase todo ponto, e também que, se um atrator possui todos expoentes de Lyapunov estritamente negativos num conjunto de medida atratora maior que zero, então seu suporte é uma órbita periódica assintoticamente estável.
Title in English
Bifurcations SUCCESSIVE SYSTEMS IN INFINITE DIMENSION
Keywords in English
statistical mechanics
Abstract in English
Here, a definition of an attractor as an invariant measure is given based on Ergodic Theory, foundations of Statistical Mechanics and some examples. Chaos is related to the presence of an attractor with metric entropy grater zero. It is proved that a chaotic attractor has positive Lyapunov exponents almost everywhere, and that, if an attractor has every Lyapunov exponents less than zero in a set of nonzero measure then the support set of the attractor is an asymptotic stable periodic orbit.
 
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Publishing Date
2012-10-01
 
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