The UB Group of Dynamical Systems aim at describing evolution problems with respect to time, be them given by ordinary or partial differential equations or by discrete transformations.

Both the qualitative and the quantitative aspects of the systems fall in this study. A key idea is the consideration of that evolution in the phase space or, better, in the phase-and-parameter space, to take into account the dependence of the system with respect to parameters.

Both theoretical and applied aspects are considered.

The topics studied by the group fall in the following items

• Invariant manifolds
• Identification and analysis of invariant objects through Computer Assisted Proofs (CAP)
• Integrability of Hamiltonian systems
• Symplectic maps and perturbations
• Reducibility of Hill- Schrodinger's equations and discrete Schrodinger operators
• Study of diffeomorphisms in dimension 3: bifurcations, invariant objects and attractors
• Study of the relative abundance of strange attractors in the dissipative Henon map
• Study of the invariant manifolds at infinity in problems of Celestial Mechanics
• Study of the existence and stability of periodic and quasi-collision orbits in Celestial Mechanics problems
• Effective stability domains near $L_4$ and $L_5$ and heteroclinic connections to the centre manifold of $L_1$
• Determination of spatial trajectories using invariant manifolds
• LEO--GEO connecting orbits using Moon gravity assists and libration point orbits
• Satellite formation flying
• Dynamics of planetary rings
• Analysis of models of the ocean, atmosphere and problems of climatology using dynamical system techniques
• Detection of homo/heteroclinic orbits and strange attractors in fluid mechanics
• Study of the hydrogen atom under the action of crossed electric and magnetic fields
• Study of the Julia and Fatou sets for holomorphic dynamical systems: rational, transcendental entire or meromorphic maps, using quasiconformal surgery, symbolic dynamics and complex analysis
• Study of parameter plane for certain one parameter families of holomorphic maps