Estudi qualitatiu i numèric de sistemes dinàmics en baixa dimensió

The project has the next three subprojects, with the following objectives: Combinatorial Dynamics in dimension one: (1) Characterization of the elements with maximal entropy among the Markov matrices of order n assopciated to periodic orbits of tree maps. (2) Characterization of the forcing relation for patterns of continuous tree maps. (3) Dynamics of Bowen-Series maps. (4) Characterizaiton of the rotation theory for continuous graph maps in graphs with a unique circuit; and its application to the characterization of their sets of periods. (5) Study of the border-collision bifurcations in the non differentiable locally unimodal case and its applications. Triangular maps and their applications: (1) Numerical approximation of invariant manifolds of invariant curves. (2) Computational techniques for invariant objects based in wavelets. Application to the computation of SNA. (3) Study of the SNA without quasiperiodic perturbation and their relation with the rotation theory