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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2000.tde-20210729-123149
Document
Author
Full name
Roberto Ferraz Barreto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Title in Portuguese
Bifurcações de linhas de curvatura em torno de conexões de pontos umbílicos
Keywords in Portuguese
Equações Diferenciais
Abstract in Portuguese
Nesta tese damos continuidade ao trabalho de Gutierrez e Sotomayor sobre bifurcações de codimensão um de conexões de pontos umbílicos de superfícies compactas. São estudadas bifurcações de codimensão dois de conexões de pontos umbílicos darbouxianos de tais superfícies. Encontra-se condições para que a aplicação de Poincaré relacionada às conexões umbílicas se desdobre genericamente a dois parâmetros, quando a superfície é deformada em uma vizinhança da conexão umbílica. Obtém-se um diagrama de bifurcação equivalente ao diagrama da bifurcação de Hopf de codimensão dois, para pontos de equilíbrio de campos vetoriais no plano
Title in English
not available
Abstract in English
In this thesis we extended the work of Gutierrez and Sotomayor concerned with codimension one bifurcation of umbilical connections of compact surfaces. Bifurcations of codimension two of connections joining darbouxian umbilical points are considered. We state conditions to gusrantee that the Poincaré map related to the umbilic connections can be generically unfolded with two parameters when the surface is perturbed in a neighborhood of the umbilic connection. One obtain a bifurcation diagram equivalent to the diagram of the Hopf bifurcation of codimension two of equilibrium points of vector fields in the plane
 
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Publishing Date
2021-07-29
 
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