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Research topics

Several different areas are currently subject of research.

  1. Dynamical Systems and Stability.

    Subjects:
    1. The period function of plane centers, in relation to  the existence and/or uniqueness of critical orbits, convexity, monotonicity partitions.
    2. Existence, uniqueness, multiplicity of limit cycles of planar systems.
    3. Perturbation problems for hamiltonian systems, in the line of Poincaré-Birkhoff theorems.
     
  2. Control Theory.

    The research of the group is devoted to problems of control and optimal control of differential equations, and to related problems of differential games. In particular, the recent activity of research has been focused on:

    • Application of the dynamic programming method and study of the corresponding Bellman/Isaacs equation in the viscosity sense, concerning with
      - optimal control problems and differential games with hybrid thermostatically switching dynamics;
      - optimal control of more general ordinary differential systems with hysteresis effects, and applications.
    • Mean field games and applications.
    • Null controllability of semilinear parabolic equations with hysteresis.

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