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Doctoral Thesis
DOI
Document
Author
Full name
Maria Aparecida Soares Ruas
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1983
Supervisor
Committee
Favaro, Luiz Antonio (President)
Figueiredo, Gil Vicente Reis de
Guimaraes, Luiz Carlos
Loibel, Gilberto Francisco
Soares, Marcio Gomes
Title in Portuguese
C l DETERMINAÇÃO FINITA E APLICAÇÕES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Not available
Keywords in English
Not available
Abstract in English
This work is concerned with the analysis of the conditions for a map-germ to be finitely determined and of the degree of determinacy. In Chapters II and III, we obtain estimates for the degree of Cr-G-determinacy, where G = K,R and C. These estimates are exact in many cases, as for instance, in the following proposition: "Let f : (Rn, 0) → (Rp,0) be given by: {ui = xi i = 1, ..., p-k, yj = fj (x1, ... xp-k, xp-k+1, ..., xn), j = 1, ... k, where fj is homogeneous of degree sj. If f is G-determined or more generally if IG is elliptic then f is (s+l-1)-Cl-G determined, with s = max sj". The groups of interest in Chapters IV and V are A and C0-A. We obtain relations among tangent spaces to the orbits,and we apply them to problems of topological triviality, modality and normal forms, The main result in Chapter IV is a sufficient condition for topological triviality, that applies to map-germs not necessarily weighted-homogeneous. In Chapter V we deal with A-finitely determined germs with the property that the A-orbit is open in the K-orbit. As an application of the results, we obtain the classification of all f : (R2,0) → (R2,0) of type Σ1 and Σ2, 0 having that property.
 
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Publishing Date
2019-11-19
 
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