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- Joan C. Artés, Alex C. Rezende, Regilene D. S. Oliveira
- I. J. Bifurcation and Chaos
- 2013

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, Hilbert, 1902], are still open for this family. In this article we… (More)

- Regilene D. S. Oliveira, Alex C. Rezende
- Applied Mathematics and Computation
- 2013

In the qualitative theory of ordinary differential equations, we can find many papers whose objective is the classification of all the possible topological phase portraits of a given family of differential system. Most of the studies rely on systems with real parameters and the study consists of outlining their phase portraits by finding out some conditions… (More)

- Hans-Otto Walther, Xiaobiao Lin, +72 authors Marian Wiercigroch
- 2011

of Talks In the multiple authors case, the name with * is the speaker. Abstract: (Preliminary report) We examine the asymptotic states of symmetric solutions to ∆u − grad W (u) = 0, u : R n → R n constructed by Alikakos and Fusco. Here W is equivariant under a finite reflection group and has n + 1 nondegenerate minima. Passing to the limit as x → ∞ in… (More)

- Joan C. Artés, Alex C. Rezende, Regilene D. S. Oliveira
- I. J. Bifurcation and Chaos
- 2014

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, Hilbert, 1902], are still open for this family. Our goal is to… (More)

We study germs of pairs of codimension one regular foliations in R 3. We show that the discriminant of the pair determines the topological type of the pair. We also consider various classifications of the singularities of the discriminant.

- Joan C. Artés, Regilene D. S. Oliveira, Alex C. Rezende
- I. J. Bifurcation and Chaos
- 2016

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