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Doctoral Thesis
DOI
10.11606/T.55.2013.tde-11072013-165027
Document
Author
Full name
Iris de Oliveira Zeli
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Manoel, Miriam Garcia (President)
Mello, Luis Fernando de Osório
Saia, Marcelo José
Silva, Paulo Ricardo da
Teixeira, Marco Antonio
Title in Portuguese
Teoria de forma normal para campos vetoriais reversíveis equivariantes
Keywords in Portuguese
Antissimetria
Belitskii
Forma normal
Ressonante
Reversível equivalente
Simetria
Transversal completa
Abstract in Portuguese
Neste trabalho, apresentamos um método algébrico para obter formas normais de campos vetoriais reversíveis equivariantes. Adaptamos o método clássico de Belitskii-Elphick, usando ferramentas da teoria invariante para estabelecer fórmulas que consideram as simetrias e antissimetrias como ponto de partida. Mostramos que este método, mesmo sem simetrias, possui uma estreita relação com o método da transversal completa da teoria de singularidades. Com as ferramentas desenvolvidas nesta tese, a forma normal obtida e uma série formal que não depende do cálculo do kernel do chamado operador homológico. Formas normais para duas classes de campos, ressonantes e não ressonantes, são apresentadas, para diferentes representações do grupo 'Z IND. 2' x 'Z IND. 2' cuja linearização tem uma parte nilpotente de dimensão 2 e uma parte semi-simples com autovalores puramente imaginários
Title in English
Normal form theory for reversible eqauivariant vector fields
Keywords in English
Belitskii
Complete transversals
Normal form
Resonant
Reversible equivariant
Reversing symmetry
Symmetry
Abstract in English
We give an algebraic method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method by Belitskii-Elphick using tools from invariant theory to establish formulae that take symmetries into account as a starting point. We show that this method, even without symmetries, has a close relation to complete transversal of singularities theory. Applying the method developed in this thesis, the resulting normal form is a formal series which does not depend of the computation of the kernel of the so called homologic operator. Normal forms of two classes of non-resonant and resonant cases are presented, for dierent representations of the group 'Z INT. 2' x 'Z INT. 2' - with linearization having a 2 - dimensional nilpotent part and a semisimple part with purely imaginary eigenvalues
 
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IrisRevisada.pdf (698.23 Kbytes)
Publishing Date
2013-07-12
 
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