• Averaging theory, Melnikov method, Lyapunov-Schmidit reduction, Relaxation Oscillation theory, and other tools to study and detect invariant sets.
  • Chebyshev systems with positive accuracy and their applications in dynamics.
  • Hidden dynamics, regularization and pinching of Filippov and non Filippov systems.
  • Singular perturbation problems and their relation with regularization of piecewise smooth vector fields.
  • Typical cycles and global dynamics of piecewise smooth vector fields.
  • Sliding dynamics and chaos.
  • Invariant measures for piecewise smooth vector fields.
  • Differential Inclusions.