The group is formed by researchers from the fields of mathematics, physics and engineering and works with other groups of a technological nature. Its main lines of research can be summarized as follows:

1. Homomorphic dynamics and more specifically the study of holomorphic iteration in the unit disk or fractional iteration, linked to holomorphic vector fields in the semi-complete unit disc. As a non-autonomous version of these processes are studied the so-called Loewner chains.
2. Normal forms of degenerate fields and applications, and in particular the development of both analytical and computational techniques that allow, for example, calculate the hypernormal form of a singularity.
3. Global problems of piecewise linear systems, with emphasis on planar and three-dimensional continuous systems, systems with discontinuities are also considered.
4. Hamiltonian systems with symmetry and non-holonomic systems. In this context we study the relationship between stability and the minimizer of the functional nature of the action for solutions to the problem of three bodies, in particular, deals pe the problem of solutions of 8 "satellites" and its relationship to the original solution of Chenciner and Montgomery.
5. Numerical techniques adapted to dissipative partial differential equations. Particular combinations of integrating temporary and spatial discretizations that can estimate the inherent errors are also studied.