Integrability and Chaos - algebraic and geometric approach

Tomasz Stachowiak

Published 2008-10-16, updated 2008-10-31Version 2

This thesis presents two descriptions of complexity in dynamical systems. The algebraic approach deals with the differential Galois group theory and its restrictions on integrability. The geometric part is a formulation of dynamics in the language of differential geometry with particular application to Lyapunov exponents and variational equations. The algorithm for calculating the Lyapunov spectrum is illustrated with three examples.