My main research interest is dynamical systems, specially the qualitative theory of differential equations, with emphasis on stability and bifurcations. My particular interests include dynamical properties near heteroclinic networks that become generic in special classes of equations: symmetric, reversible and conservative.

The dynamics near a network deserves a more specific description than the dichotomy: regular dynamics vs chaos; in the latter case, generically the distant future of solutions near the network is practically inaccessible and may only be described in probabilistic and ergodic terms. The aim of my research is to verify the convergence of spatial averages associated to trajectories that remain near the networks for all time. I would like to estimate the size of the set of points persistently close to a given connection in the network. This will provide useful information about nearby dynamics and visibility of each cycle. The main question in my research is the Takens' Last Problem: whether there are persistent classes of smooth dynamical systems such that the set of initial conditions which give rise to orbits with historical behaviour has positive Lebesgue measure.

My research builds on recent results by Labouriau, Kiriki and myself, on the dynamics near symmetric heteroclinic networks.