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1	A construção do grau topológico e sua aplicação a um sistema diferencial não linear com condições de contorno / The construction of the topological degree and its application to a nonlinear differential system with boundary conditions Peixoto, Adriano Leandro da Costa 06 May 2014 (has links) O principal objetivo deste trabalho é apresentar a construção do grau topológico em dimensão finita e infinita. Veremos, também, algumas de suas propriedades e aplicações topológicas, como o clássico Teorema de ponto fixo de Brouwer. Seguindo o que fizeram Manàsevich e Mawhin no artigo ``Periodic Solutions for Nonlinear Systems with p-Laplacian-Like Operators}. Journal of Differential Equations, vol. 145, p. 367-393, 1998\'\', vamos provar a existência de soluções para um sistema diferencial não linear com condições de contorno, usando, entre outras ferramentas, o grau topológico. / The main purpose of this work is the construction of the topological degree in finite and infinite dimension. In addition, we will see some of its properties and topological applications. Following the approach of Mannàsevich and Mawhin in the paper ``Periodic Solutions for Nonlinear Systems with p-Laplacian-Like Operators. Journal of Differential Equations, vol. 145, p. 367-393, 1998\'\', we will prove the existence of solutions for a nonlinear differential system with boundary conditions, using, among other tools, the topological degree. Brouwer degree Degree theory Grau de Brouwer Grau de Leray-Schauder Leray-Schauder degree Teoria do grau
2	O Método do Averaging via Grau de Brouwer para determinar o número de ciclos limites de um centro 4-dimensional em sistemas de controle. / Bifurcation of Limit Cycles from a 4-dimensional Center in Control System MALAQUIAS, Arianny Grasielly Baiao 30 March 2010 (has links) Made available in DSpace on 2014-07-29T16:02:18Z (GMT). No. of bitstreams: 1 Dissertacao Arianny Grasielly Baiao Malaquias.pdf: 551063 bytes, checksum: c96bb635153e7e0b5f3ae1b8cd01d621 (MD5) Previous issue date: 2010-03-30 / In this work, we studying the Averaging Method via Brouwer Degree for upper bound the number of limit cycle that can bifurcate from a center type singularity of a diferential equation system. After that, we give concrete examples this upper bound can be realized. / Nesta dissertação, estudaremos o Método do Averaging via Grau de Brouwer para determinar o número de ciclos limites que podem bifurcar de uma singularidade do tipo centro de um sistema de equações diferenciais. Além disso, mostramos através de exemplos concretos que esta cota superior pode ser realizada
3	Hopf Bifurcation from Infinity in Asymptotically Linear Autonomous Systems with Delay Biglands, Adrian Unknown Date No description available.
4	The degree theory and the index of a critical point for mappings of the type (<em>S</em><sub>+</sub>) Oinas, J. (Janne) 31 May 2007 (has links) Abstract The dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type. A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function. A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point. Brouwer degree Browder degree Leray-Schauder theory Skrypnik degree degree theory index of a critical point index of a singular point mapping degree mappings of monotone type nonlinear analysis nonlinear functional analysis rotation of vector field the Brouwer-Hopf theory the Browder theory the Leray-Schauder degree the Skrypnik theory topological degree

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