Maria Joana Torres

Shades of hyperbolicity for Hamiltonians

We prove that a Hamiltonian system is globally hyperbolic if any of the following statements hold: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification property. Moreover, we prove that, for a C2-generic Hamiltonian H, the union of the partially hyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset of M. As a consequence, any robustly transitive regular energy hypersurface of a C2-Hamiltonian is partially hyperbolic. Finally, we prove that stable weakly-shadowable regular energy hypersurfaces are partially hyperbolic.

Combinatorial stability of non-deterministic systems

We introduce and study, from a combinatorial-topological viewpoint, some semigroups of continuous non-deterministic dynamical systems. Combinatorial stability, i.e. the persistence of the combinatorics of the attractors, is characterized and its genericity established. Some implications on topological (deterministic) dynamics are drawn.

r-Regularity

We provide a characterization of

Stability of Non-deterministic Systems

r

Introdução aos sistemas dinâmicos

r-regular sets in terms of the Lipschitz regularity of normal vector fields to the boundary.

Hyperbolicity and stability for Hamiltonian flows

For a class of semigroups of stochastic dynamical systems, x Px, where x denotes a state and Px the state probability transition, we relate its spectral stability to the combinatorial stability of the underlying non-deterministic dynamics, associated with the point-set map x supp(Px).

Smoothness of Boundaries of Regular Sets

A space of non-deterministic dynamical systems of Markov type on compact manifolds is considered. This is a natural space for stochastic perturbations of maps. For such systems, both the combinatorial stability, of the periodic attractors, and the spectral stability, of the invariant measures, are characterized and its genericity established.

On the periodic orbits, shadowing and strong transitivity of continuous flows

This paper focuses on the concept of the seamless mobility (provided by vertical handover mechanisms) in heterogeneous Future Internet Networks in the context of the HURRICANE project. We discuss future open collaborative network architectures and propose a set of entities that ensure seamless mobility and service continuity, from infrastructural/operational and business standpoints: an 802.21-like implementation of vertical handover, supported by an innovative business modelling software package, which replaces the traditional operations support stack with a more dynamic, marketplace-oriented system. We also discuss, an approach to distributed, policy-based, vertical handover management and a model for such policies, based on the monitorization and analysis of Call Detail Records that reveals users’ behavioural patterns and allows personalization.