Research

The main objectives of our research lines are:

  • Non-Uniformly Hyperbolic Dynamics and 2-Dimensional Strange Attractors: Study of heterodimensional cycles associated with geometric structures (called blenders) that involve a high number of new transitions and dynamical complexity; Determination of homoclinic tangencies that explain the persistence of non-hyperbolic strange attractors.
  • Singularities and Unfoldings of Vector Fields: Topological classification of singularities, incorporating new 4-dimensional topological types; Identification of those singularities that organize the chaotic dynamics; Analysis of singularities that arise naturally in coupled systems and that are associated with synchronization phenomena; Study of the Hopf-Zero, Hopf-Bogdanov-Takens and 4-dimensional nilpotent singularities.
  • Polynomial Differential Systems: Multiplicity of limit cycles; Study of quasi-homogeneous systems in dimension greater than or equal to three; Obtaining algebraic limit cycles in piecewise linear systems.
  • Applied Dynamic Systems: Numerical studies to the mechanisms associated with spike-adding phenomena in neuronal models and the analysis of the role that homoclinic bifurcations play in these models; Study of the dynamical systems related to climate processes.