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Non-smooth dynamical systems: qualitative theory and structural stability

Abstract

The theory of Non-Smooth Dynamical Systems is a subject that has been developing very fast in recent years, mainly due to its strong relationship with other fields of science. Establish clear notions of stability and bifurcations that are consistent with the real world has been an arduous and challenging task for mathematicians, physicists and engineers. There is very little done with respect to the study of generic bifurcations and normal forms for such systems.Our goal is to study is a non-smooth version of Hilbert's 16th problem for discontinuous systems, mainly studying the birth of limit cycles when considering non-smooth perturbations of linear smooth centers. The existence of such orbits is of fundamental importance in physical models based on discontinuous equations.The basic tool in this study is the Averaging Method. which applies almost directly to the non-smooth systems. In particular, we also show that the averaged equation is compatible with the discontinuity line of the system. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GRAMA, LINO; MARTINS, RICARDO MIRANDA. A brief survey on the Ricci flow in homogeneous manifolds. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 9, n. 1, p. 37-52, JUN 2015. Web of Science Citations: 0.
MARTINS, RICARDO MIRANDA; MEREU, ANA CRISTINA; OLIVEIRA, REGILENE D. S. An estimation for the number of limit cycles in a Lienard-like perturbation of a quadratic nonlinear center. NONLINEAR DYNAMICS, v. 79, n. 1, p. 185-194, JAN 2015. Web of Science Citations: 3.
MARTINS, RICARDO MIRANDA; MEREU, ANA CRISTINA. Limit cycles in discontinuous classical Lienard equations. Nonlinear Analysis: Real World Applications, v. 20, p. 67-73, DEC 2014. Web of Science Citations: 15.

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