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1	Movimentos sob atração focal em campos vetoriais planares / Motions under focal attraction in planar vector fields MARTINS, Tiberio Bittencourt de Oliveira 29 August 2008 (has links) Made available in DSpace on 2014-07-29T16:02:23Z (GMT). No. of bitstreams: 1 Dissertacao Tiberio Bittencourt.pdf: 638703 bytes, checksum: b4eef7616f38b5efeb40a4c5c26e0b75 (MD5) Previous issue date: 2008-08-29 / In this work, we develop the article On the motion under focal attraction in a rotating medium , of J. Sotomayor, which deals with a bidimensional differential system that model the following Biological problem: in a shallow recipient with circular section, with liquid in, spinning with angular speed ω, there are platyhelminthes, flatworms organisms, they are attracted by a fix lighting point near of the border of the recipient and they swim with a speed v in the direction of the this point. The problem is to show that there exists an equilibrium point where platyhelminthes go to cluster by the time passing. It s analyzed the dynamic of the model: existence of critical points and stability of the system and bifurcations. We analyzed three modifications of this system too. In the last part, it s discussed a criterium for non existence of periodic orbits of a planar vector fields in a simply connected region. / Neste trabalho, desenvolvemos o artigo On the motion under focal attraction in a rotating medium de J. Sotomayor [9] que trata de um sistema de equações diferenciais bidimensional que modela o seguinte problema na Biologia: num recipiente raso de seção circular, com líquido, girando a uma velocidade angular ω, existem platelmintos, organismos vermiforme, eles s ao atra´ıdos por um ponto luminoso fixo perto da borda do recipiente e nadam com uma velocidade v em direçãoa este ponto. O problema é mostrar que existe um ponto de equilíbrio onde os platelmintos vão se aglomerar com o passar do tempo. É analisada a dinâmica da modelagem: existência de pontos de equilibrio e estabilidade do sistema e bifurcaçoes. Analisamos tambem tres modificaçoes desse sistema. Na parte final, e discutido um criterio para determinaçao da ausencia de orbitas periodicas em campos vetoriais planares. Campos vetoriais planares Biologia Equações diferenciais bidimencionais Dinâmica de modelagem Platelmintos
2	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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Movimentos sob atração focal em campos vetoriais planares / Motions under focal attraction in planar vector fields

Feigenbaum Scaling