Márcio Ricardo Alves Gouveia

• Abstract

  Poincare's work was the forerunner of modern theory of dynamical systems. Since its introduction, this theory has grown and matured, becoming an important and much studied area of mathematics. The main objective of this project is to deepen the knowledge in the following areas of dynamical systems:1 - Renormalization Theory and Cherry flows.2 -Rigidity for one-dimensional dynamical system…

  Dynamical properties of some classes of interval maps, AP.R
• ICTP-ESF School and Conference in Dynamical Systems, AR.EXT

• Abstract

  In this project, we will start the study on the theory of continuous and discrete dynamical systems. We will study the fundamental concepts and results of the theory.

  Introduction to the dynamical systems theory, BP.IC

• Abstract

  In this project we intend to start studies on interesting mathematical objects called fractals. We will study its formation processes and its dynamic behaviors, some of its properties such as Hausdorff dimension. Finally, we will try to understand a little bit about Julia and Mandelbrot sets and some properties that they present. (AU)

  Fractal geometry: an introduction, BP.IC

• Abstract

  In this project we will study the basic concepts of discrete dynamical systems, which will serve as a tool for establishing the knowledge and also as the basis for the study of important results and techniques from the dynamical system area, especially for nonlinear systems, which are not seen during the graduation. Some topics that will be covered are the concepts of periodic orbits, bif…

  Chaos: an introduction to the dynamical systems theory, BP.IC

(Only some records are available in English at this moment)

• Abstract

  We are going to study the dynamics of maps acting on the interval, with a unique point of discontinuity, where the one-sided derivatives exists, and whose derivative is positive and strictly smaller than one everywhere. Such applications are called dissipative Lorenz maps. We will also assume that those Lorenz maps have criticality. More precisely we will be interested on the rigidity cla…

  Rigidity of dissipative Lorenz maps with criticality, BE.PQ

• Abstract

  Investigate the existence of periodic orbits for functions defined on a compact manifold, using as main tools, the Lefschetz numbers and Nielsen numbers. For this we attempt characterize the set of periods of a such function. (AU)

  Existence of periodic orbits using Lefschetz and Nielsen numbers theory, BE.PQ