The first part of the talk is about the multidimensional generalization of the hyperbolic periodic orbits and their invariant manifolds in Hamiltonian systems. Those manifolds play an essential roll to understand the transport and the dynamics in multidimentional phase space.

The second part of the talk is about quantum dynamics and its connection with classical dynamics. The time dependent variational principle and coherent states has been successfully used to calculate the evolution of quantum systems with classical analog. Some remarkable examples are chemical systems with large dimension. Based on this approach, we explore the possibility to calculate the long term dynamics of a experimental time dependent spin chain.

* Francisco Gonzalez Montoya, Centro International de Ciencias AC, Mexico and University of Leeds, UK