Licenciatura em Matemática (Sede)
URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24
Siglas das Coleções:
APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso
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3 resultados
Resultados da Pesquisa
Item O floco de neve de Koch e suas propriedades: funções contínuas sem derivada em ponto algum(2024-07-31) Santos, Vivian Maria dos; Clemente, Rodrigo Genuino; http://lattes.cnpq.br/4351609162717260; http://lattes.cnpq.br/0771390443429539In this work, we present the existence of real continuous functions that have no derivative at any point. For this, we use the function developed by the mathematician Helge von Koch as an example, demonstrating that this function is continuous at all points but not differentiable at any point. We show how this curve is constructed and discuss itsproperties. To highlight these facts, many constructions of such functions are based on infinite series of functions. Therefore, we introduce some fundamental concepts and results from Mathematical Analysis, specifically, Sequences and Series of functions, which allow us to investigate the continuity and differentiability properties. Finally, we will comment on an interesting result that reveals that the set of these functions constitutes a dense and residual set in the complete metric space, meaning that these functions exist abundantly. The proof of this statement is based on Baire’s Theorem, which generally states that any countable union of thin sets is so small that its complement is dense.Item Noções de dinâmica unidimensional e Teorema de Lie-York(2022-02-24) Barbosa, Caio Vinícius de Araújo; Silva, Eberson Ferreira da; http://lattes.cnpq.br/9911410714371158; http://lattes.cnpq.br/7154067317344387In this work we present notions of one dimensional dynamical systems and a result known as Li-Yorke's Theorem. For this, we initially deal with continuous functions and analysis results of the line. Then we talk about xed and periodic points and their relationships with the orbits of nearby points.Item O Teorema de Baire e suas aplicações na Análise Funcional(2019-07-29) Albuquerque, Anne Caroline Carneiro de; Silva, Clessius; http://lattes.cnpq.br/2401078773322406; http://lattes.cnpq.br/5028414803312146In this work, we will present the applications of Baire’s Theorem to Functional Analysis, more specifically to the classic results of this area, Banach Steinhaus Theorem, Open Application Theorem and Closed Graph Theorem.