Dynamical systems in cosmology and astrophysics

Abstract: General relativity is today an important branch of physics. It has, since its publication at the beginning of this century, changed from being of more mathematical than physical interest to one of the most active experimental fields in physics. It is needed for today's technology as well as for describing astrophysical phenomena and the structure of the universe. However, many aspects of the theory are not yet fully understood theoretically.In this thesis, the general relativistic gravitational field equations are studied using the theory of dynamical systems. Such systems cover a wide variety of interesting phenomena in cosmology and astrophysics. For example, special spherically symmetric models yield dynamical systems that are important for understanding gravitational collapse, cosmic censorship, and non-linear density fluctuations in standard cosmology. Various techniques are discussed and developed. Analytic and numerical methods are combined in order to obtain a global picture of the solution space of the systems of the differential equations considered. These results are then used to extract physical information.