2008/10/16 by Tomasz Stachowiak, Stachowiak, Tomasz
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.0810.2968
openalex publication_date 2008/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.