Efficient Approximation Methods for the Global Long-Term Behavior of Dynamical Systems - Theory, Algorithms and Examples

By Peter Koltai

In this thesis three new transfer operator based approaches are developed for the analysis of the long-term behavior of dynamical systems. First, a sparse grid discretization is derived in order to deal with the "curse of dimension". The second method considers the infinitesimal generator of the transfer operator semigroup for continuous-time systems. The third method uses mean field theory to describe the dynamics of subsystems; here the main attention is devoted to conformation analysis in molecular dynamics. Further, conditions are derived such that the Galerkin projection of the transfer operator can be related to a small random perturbation of the underlying system.

• Format: Paperback
• Language: English
• ISBN: 3832527524
• ISBN13: 9783832527525
• Release Date: December 2010
• Publisher: Logos Verlag Berlin
• Length: 168 Pages