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DY: Fachverband Dynamik und Statistische Physik
DY 6: Nonlinear Dynamics, Synchronization and Chaos
DY 6.1: Vortrag
Montag, 16. März 2020, 10:00–10:15, ZEU 147
Estimating Lyapunov exponents in billiards — George Datseris1,2, •Lukas Hupe1,2, and Ragnar Fleischmann1,2 — 1Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen — 2Faculty of Physics, Georg-August-Universität Göttingen, 37077, Göttingen, Germany
Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it.