Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

A Formalised Model of the Information and Materials Handling Activities in the Construction Process

A model of the information and material activities that comprise the overall construction process is presented, using the SADT activity modelling methodology. The basic model is further refined into a number of generic information handling activities such as creation of new information, information search and retrieval, information distribution and person-to-person communication. The viewpoint could be described as information logistics. This model is then combined with a more traditional building process model, consisting of phases such as design and construction. The resulting two-dimensional matrix can be used for positioning different types of generic IT-tools or construction specific applications. The model can thus provide a starting point for a discussion of the application of information and communication technology in construction and for measurements of the impacts of IT on the overall process and its related costs.