Qualitative Theory of Differential Equations

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Although during the last 20 years we work in so many different problems related with qualitative theory of differential equations, during the last few years we center most of our interest in problems surrounding the well-known 16th Hilbert′s problem and the Jacobian Conjecture. We bring out our work on the Markus-Yamabe conjecture, Liapunov constants, center-focus problem, hamiltonian perturbations, abelian integrals, isochronicity, uniqueness of limit cycles, etc.

Others kind of problems we are also interested are general theory of polynomial systems, control theory, study of singularities via blow ups, non differentiable dynamical systems, structural stability, quadratic polynomial systems, etc.

Some researchers with whom we work together are: C. Christopher, F. Dumortier, J.P. Françoise, H. Giacomini, C. Li, D. Shafer, J. Sotomayor, M.A. Teixeira, X. Zhang.