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Master's Dissertation
DOI
10.11606/D.45.2013.tde-21012015-214244
Document
Author
Full name
Bruno de Paula Jacóia
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Tello, Jorge Manuel Sotomayor (President)
Garcia, Ronaldo Alves
Zanata, Salvador Addas
Title in Portuguese
Estabilidade estrutural dos campos vetoriais seccionalmente lineares no plano
Keywords in Portuguese
Campos de vetores lineares por partes
Compactificação de Poincaré
Estabilidade estrutural
Abstract in Portuguese
Estudamos uma classe de campos de vetores seccionalmente lineares no plano denotada por X. Tais campos aparecem frequentemente em modelos matemáticos aplicados à engenharia. Baseados no trabalho de J. Sotomayor e R. Garcia [SG03], impondo condições sobre as singularidades, órbitas periódicas e separatrizes, definimos um conjunto de campos de vetores que são estruturalmente estáveis em X. Provamos que esse conjunto é aberto, denso e tem medida de Lebesgue total em X, o qual é um espaço vetorial de dimensão finita.
Title in English
Structural stability of piecewise-linear vector fields in the plane
Keywords in English
Piecewise-linear vector fields
Poincaré compactification
Structural stability
Abstract in English
We study a class of piecewise-linear vector fields in the plane denoted by X. These vector fields appear often in mathematical models applied to Engineering. Based on Jorge Sotomayor and Ronaldo Garcia paper [SG03], we impose conditions on singularities, periodic orbits and separatrices, to define a set of vector fields structurally stable in X. We give a proof that this set is open, dense and has full Lebesgue measure in X, that is a finite dimensional vector space.
 
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Publishing Date
2015-04-08
 
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