Covariant Lyapunov vectors for rigid disk systems

Author(s)
Hadrien Bosetti, Harald Posch
Abstract

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.

Organisation(s)
Computational and Soft Matter Physics
Journal
Chemical Physics
Volume
375
Pages
296-308
No. of pages
13
ISSN
0301-0104
DOI
https://doi.org/10.1016/j.chemphys.2010.06.010
Publication date
2010
Peer reviewed
Yes
Austrian Fields of Science 2012
103008 Experimental physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/0fe66db6-094d-49a7-a3c6-c0c6857c9479