The group’s current research topics include:
- Invariant objects in real and complex dynamical systems (periodic orbits, invariant tori, normally hyperbolic invariant manifolds).
- Dynamics of conservative systems, Arnold diffusion, invariant manifolds theory and exponentially small phenomena, homoclinic tangencies and Newhouse phenomena.
- Strange attractors.
- Celestial Mechanics and astrodynamics.
- Connections to symplectic geometry.
- Infinite dimensional dynamical systems and evolution PDEs.
- Numerical and computational methods for differential equations.
- Computer assisted proofs in dynamics.
- Real and complex bifurcation theory: Stability and instability locus in parameter spaces.
- Rigidity problems in dynamical and parameter spaces.
- Numerical methods as dynamical systems.
- Quasiperiodically forced maps and nonautonomous dynamics, real and complex.
- Wandering domains in holomorphic dynamics.
- Fractal geometry of Julia sets.
- Applications to chemistry, biology and other sciences.
For more detailed topics in holomorphic dynamics check the HOLODYN page.