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Investigation of chaotic dynamical systems using the methods of Riemannian geometry
 Matejov, Dávid ; Scholtz, Martin (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we investigate a chaos in dynamical systems described by the Hamilton function using a new geometric method. At first, necessary definitions and terms are introduced, like dynamical systems, Lyapunov ex- ponents and Poncaré sections. Subsequently we deal with the new geometric method (Horowitz et al., 2007), which predicts the stability of a system un- der consideration. An extensive part is devoted to the general relativity and spinor formalism, the Newman-Penrose formalism and the theory of optical scalars. In the computational part of the thesis, we investigate the pp-waves and chaotic behaviour of geodesics in this class of space-times. All calcula- tions are done in the Python programming language, so we the chapter on numerical calculations is included. 1
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