Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Posters I

DY 10.36: Poster

Monday, March 14, 2011, 17:00–19:00, P4

Where can one observe non-hyperbolicity? — •Jian Wang, Hongliu Yang, and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Hyperbolicity is an important property of dynamical systems. Many physically relevant dynamical systems are not hyperbolic, and many of the available theoretical results have been derived under the assumption of strict hyperbolicity. Recently, a new method for determining the so-called covariant Lyapunov vectors (CLV) was introduced by F. Ginelli et al. With CLV the degree of hyperbolicity of the dynamics can be quantified. Since in a non-hyperbolical system the violation of hyperbolicity occurs only at certain locations in state space, the determination of these locations is of much interest. In this study we investigate the relationship between hyperbolicity and the covariant Lyapunov analysis along the trajectory. Our main focus lies on the relation of angles between different local CLV to the variation of local Lyapunov exponents. The positions, where non-hyperbolictiy arises, are shown.