On the Local Smoothing for the Schroedinger Equation

We prove a family of identities that involve the solutions to the free Schreodinger equation. As a consequence of these identities we shall deduce a lower bound for the local smoothing estimate and a uniqueness criterion

Extremal Coupled Map Lattices

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and power law distributions.Comment: 4 RevTeX pages, 3 eps figures. Uses psfig.sty. To be published in The European Physical Journal B (1999