We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincare map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that ...

In this paper we present the Implicit Function Theorem and some of its applications in many areas of mathematics. In chapter one we present the theorem in the most classical way. In the second chapter, we describe what a ...

Neste trabalho utilizamos a teoria qualitativa das equações diferenciais para estudar rapidamente a bifurcação de Hopf para um sistema dinâmico planar suave mediante a variação do parâmetro de controle do sistema, e a ...

Physical systems that are subject to intermittent contact/impact are often studied using piecewise-smooth models. Freeplay is a common type of piecewise-smooth system and has been studied extensively for gear systems ...

In this work we study the renormalization operator acting on piecewise smooth homeomorphisms on the circle, that turns out to be essentially the study of Rauzy–Veech renormalizations of generalized interval exchange maps ...

This thesis deals with the determination of periodic steady state of electrical networks in the time domain based on Poincaré maps and extrapolation to the limit cycle Newton methods. In particular , we consider the methods ...

Esta tesis contempla la generalización de resultados de geomtría diferencial clásica en el contexto de los sistemas locales homotópicos. En particular, se realiza la construcción del homomorfismo de Chern-Weil y el teorema ...