We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k-contact structure and k-contact Hamiltonian system. This is a generalization ...

The aim of this thesis is to give a method to produce families of complete Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k}\binom{n}{k}$ on $M\setminus \Lambda^p$, where $M$ is a Riemannian ...

The two main stability results for nearly integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning ...

We consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a two-dimensional invariant ...

Kostant gave a model for the geometric quantization via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by integrable systems ...

Quasiperiodic perturbations with two frequencies $(1/\varepsilon ,\gamma /\varepsilon )$ of a pendulum are considered, where $\gamma $ is the golden mean number. We study the splitting of the three-dimensional invariant ...

A microbial Individual-based Model (IbM) to deal with yeast populations growing in liquid batch cultures has been designed and implemented in a simulator called INDISIM-YEAST. Interesting qualitative results have already ...

In this paper we introduce a general methodology for computing (numerically) the normal form around a periodic orbit of an autonomous analytic Hamiltonian system. The process follows two steps. First, we expand the ...

The purpose of this paper is to study the dynamics near a reducible lower dimensional invariant tori of a finite-dimensional autonomous Hamiltonian system with $\ell$ degrees of freedom. We will focus in the case in ...