Marco Antonio Teixeira

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We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form¨x + f (x) ˙ x + g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m − 1)/2] limit cycles, where(More)
Brassinosteroids are a new class of plant hormones with a polyoxygenated steroid structure showing pronounced plant growth regulatory activity. This review covers their natural occurrence, biological and chromatographic methods for their detection, biosynthesis and metabolism, biological activity, structure-activity relationships and prospective(More)
In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 typical singularities(More)
(Communicated by Aim Sciences) Dedicated to Carlos Gutierrez and Marco Antonio Teixeira on the occasion of their 60th birthdays. Abstract. We study geometric properties of the integral curves of an implicit differential equation in a neighbourhood of a codimension ≤ 1 singularity. We also deal with the way these singularities bifurcate in generic families(More)
In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a(More)