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Previous issue date: 2016-02-26 / CNPq / Neste trabalho, estudaremos o conjunto de equil brios relativos n~ao-colineares do
problema de quatro corpos no plano complexo. Veremos que esse conjunto e uma
subvariedade estrati cada maximal de certa variedade alg ebrica real e provaremos a
unicidade do vetor massa normalizado associado a cada ponto dessa subvariedade. Por
meio de transforma c~oes de regulariza c~ao, reduziremos a teoria de bifurca c~oes de equil brios
relativos ao estudo de uma correspond^encia alg ebrica entre variedades reais. Atrav es dos
teoremas de nitude para variedades alg ebricas reais, provaremos que existe uma cota para
o n umero de classes de equil brios relativos n~ao-colineares v alida para todas as massas
positivas no complementar de um subconjunto alg ebrico pr oprio no espa co das massas. / In this work, we study the set of non-collinear relative equilibria in the fourbody
problem in the complex plane. We will see that this set is a maximal
strati ed submanifold in a real algebraic variety and prove the uniqueness of the
normalized vector mass associated with each point of this submanifold. By means of
regularization transformations, we reduce the bifurcation theory to the study of an
algebraic correspondence between real varieties. Through the theorems of niteness
for real algebraic varieties, we prove that there is an upper bound for the number of
a ne classes of non-collinear relative equilibria which holds for all positive masses in the
complement of a proper, algebraic subset of all masses.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufpe.br:123456789/17992 |
| Date | 26 February 2016 |
| Creators | LOPES, Juscelino Grigório |
| Contributors | http://lattes.cnpq.br/0559184209749319, LEANDRO, Eduardo Shirlippe Góes |
| Publisher | Universidade Federal de Pernambuco, Programa de Pos Graduacao em Matematica, UFPE, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFPE, instname:Universidade Federal de Pernambuco, instacron:UFPE |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil, http://creativecommons.org/licenses/by-nc-nd/3.0/br/, info:eu-repo/semantics/openAccess |
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