Symmetry properties of orthogonal and covariant Lyapunov vectors and their exponents
Abstract
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 socalled covariant vectors, comoving with the linearized flow in tangent space. Taking a simple spring pendulum and the HénonHeiles system as examples, we demonstrate the consequences of symplectic symmetry and of timereversal invariance for such vectors, and study the transformation between different parameterizations of the flow.
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 DOI:
 10.48550/arXiv.1107.4032
 arXiv:
 arXiv:1107.4032
 Bibcode:
 2011arXiv1107.4032P
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Classical Physics
 EPrint:
 8 pages, 6 Figures