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Classificação de centros Hamiltonianos polinomiais biquadrados, e isocronicidade trivial versus formas canônicas para aplicações polinomiais no plano de Jacobiano unitário
(Universidade Federal de São Carlos, 2022-10-10)
This work, we classify a non- degenerate center at the origin of a planar Hamiltonian system associated to a function of the form $H(x,y)=A(x)+B(x)y^2 + C(x)y^4$, where $A$, $B$ and $C$ are polynomials. After seing a ...
Classes características de variedades topológicas e generalizadas
(Universidade Federal de São Carlos, 2022-03-24)
In this work, we will initially present generalized bundles, a concept developed by Fadell with
the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the
context of smooth manifolds ...
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, 2022-02-14)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
Geometric invariants of groups and property R-infty
(Universidade Federal de São Carlos, 2022-01-05)
In this thesis we study property R_\infty for some classes of finitely generated groups by the use of the BNS invariant \Sigma^1 and some other geometric tools. In the combinatorial chapters of the work (4, 5, 6, 10 and ...
Um estudo de valorizações transcendentes e algébricas via polinômios-chaves e pares minimais
(Universidade Federal de São Carlos, 2022-02-24)
The main goal of this work is to study transcendental valuations and algebraic valuations. To achieve this, we use some of the main objects in Valuation Theory, such as key polynomials, truncations and minimal pairs. These ...
Estabilidade, instabilidade e fenômenos de concentração em equações de reação e difusão: uma abordagem geométrica
(Universidade Federal de São Carlos, 2022-12-07)
In this work, we adress the study of stability of a reaction-difusion equation in two domains: in a family of surfaces of revolution without boundary and in a bounded open interval whose diffusion function vanishes at a ...
Não unicidade para uma classe de operadores do tipo parabólico
(Universidade Federal de São Carlos, 2022-01-18)
In this thesis we consider the non-uniqueness for a class of parabolic operators. We will
prove that for certain real analytic perturbation of the Heat Operator there is a non unique
solution for the Initial Value Problem.
Soluções positivas para equações elípticas com operadores fracionários
(Universidade Federal de São Carlos, 2022-03-18)
In this work, we present results of existence, non-existence and multiplicity of positive
solutions to elliptic problems involving the fractional p-Laplacian operator and the
fractional Laplacian in the critical case, ...
O número de Bruce-Roberts sobre uma ICIS
(Universidade Federal de São Carlos, 2022-01-19)
In this work we study the relations between the Bruce-Roberts number, $\mu_{BR}(f,X)$, the relative Bruce-Roberts, $\mu_{BR}^{-}(f,X)$, of a function germ $f\in\mathcal{O}_{n}$ over an ICIS, $(X,0)\subset (\C^{n},0)$, and ...
Polynomial Weingarten surfaces of tubular type
(Universidade Federal de São Carlos, 2022-04-04)
This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, ...