Early works, under the supervision of Ernest Fontich, dealt about the problem of abundance of Arnold difussion in the context of analytic Hamiltonian systems. Besides proving the density of systems with exhibiting such behaviour, several tools were developed that have been used afterwards by several authors.
Related to the problem of instability, the splitting of separatrices has also been studied, both for area preserving maps and Hamiltonian systems of higher dimension.
As a consequence of these last developments, recently a prove has been found of the existence of oscillatory motions in the restricted planar circular three body problem for all values of the mass paramenter, closing a long standing problem.
- Hamiltonian systems
- Arnold diffusion
- Parabolic points and their invariant manifolds
- Splitting of separatrices
- Celestial Mechanics: oscillatory motions in several instances of the n-body problem
- Guardia, M.; Martín, P; Seara, T.M. (2015). Oscillatory motions for the restricted planar circular three body problem. Inventiones Math. DOI 10.1007/s00222-015-0591-y
- Baldomá, I; Martín, P. (2012). The inner equation for generalized standard maps. SIAM J. Appl. Dyn. Syst. 11, 1062–1097
- Martín, P.; Sauzin, D.; Seara, T. M. (2011). Exponentially small splitting of separatrices in the perturbed McMillan map. Discrete Contin. Dyn. Syst. 31, 301–372
- Baldomá, I.; Fontich, E.; de la Llave, R.; Martín, P. (2007). The parameterization method for one-dimensional invariant manifolds of higher dimensional parabolic fixed points. Discrete Contin. Dyn. Syst. 17, 835–865
- Fontich, E.; Martín, P. (2001). Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discrete Contin. Dynam. Systems 7, 61–84