I work in dynamical systems theory. Nowadays I'm mostly focused in discrete dynamical systems. In particular in integrability issues; existence of first integrals, Lie Symmetries; dynamical properties of systems with a prescribed number of first integrals; existence of periodic orbits, dense solutions in prescribed invariant sets; global stability; bifurcations, algebraic and geometrical methods. I am also interested in applications of discrete dynamical systems to mathematical biology and physics.
I have worked in the qualitative and analytic theory of Ordinary Differential Equations. In particular in topics related with the local study and bifurcation phenomena from singularities, periodic orbits and polycycles. I was also involved in center-focus problem and the study of the period function of planar ODEs.
My work is done within the Control, Dynamics and Applications Group - CoDAlab, and together with my colleagues I have also studied some problems related with the modeling, control, identification and periodic orbits of nonlinear systems with hysteresis.