Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-05-07
Chemical Physics, Volume 375, Issues 2-3, 5 October 2010, Pages 296-308
Nonlinear Sciences
Chaotic Dynamics
23 pages, 17 figures; Chemical Physics, in press, June 2010. Chem. Phys. (2010): cited as: H. Bosetti, H.A. Posch, Chem. Phys.
Scientific paper
10.1016/j.chemphys.2010.06.010
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.
Bosetti Hadrien
Posch Harald A.
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