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Doctoral Thesis
DOI
10.11606/T.55.2019.tde-02042019-144449
Document
Author
Full name
Solange Mancini
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1989
Supervisor
Committee
Ruas, Maria Aparecida Soares (President)
Carneiro, Mario Jorge Dias
Egusquiza, Eduardo Alfonso Chincaro
Favaro, Luiz Antonio
Tadini, Wilson Mauricio
Title in Portuguese
φ EQUIVALÊNCIA
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
φ-Equivalence
Keywords in English
Not available
Abstract in English
We study φ-equivalence, and the corresponding concepts of finite determinacy and transversal unfoldings. This equivalence was introduced by L. Favaro and C. Mendes who studied φ - stability. We obtain necessary and sufficient conditions for finite φ - determinacy of map-germs that apply to a special class of infinitesimally stable germs w. Building upon results of Egúsquiza for π - stable paths of mappings, we prove genericity theorems for an auxiliary equivalence relation, namely Ã-- equivalence, and for φ equivalence. The main result shows that the evolution of the singularities from a manifold N into the plane can be realized by preserving a foliation defined by a fixed Morse function φ : N → R. Moreover, the generic bifurcations are classified.
 
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SolangeMancini.pdf (2.46 Mbytes)
Publishing Date
2019-04-02
 
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