2011/07/20 by Posch, Harald A.
#Chaotic Dynamics (nlin.CD) #Classical Physics (physics.class-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1107.4032
Lyapunov exponents are indicators for the chaotic properties of a classical dynamical system. They are most naturally defined in terms of the time evolution of a set of so-called covariant vectors, co-moving with the linearized flow in tangent space. Taking a simple spring pendulum and the Hénon-Heiles system as examples, we demonstrate the consequences of symplectic symmetry and of time-reversal invariance for such vectors, and study the transformation between different parameterizations of the flow.