Integrability and Chaos - algebraic and geometric approach

Details Integrability and Chaos - algebraic and geometric approach Integrability and Chaos - algebraic and geometric approach

2008-10-16

arxiv.org/abs/0810.2968v2

Physics

Mathematical Physics

PhD thesis. 41 pages, 9 figures

Scientific paper

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.

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