Covariant Lyapunov vectors for rigid disk systems
arXiv:1005.1172 · doi:10.1016/j.chemphys.2010.06.010
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.
23 pages, 17 figures; Chemical Physics, in press, June 2010. Chem. Phys. (2010): cited as: H. Bosetti, H.A. Posch, Chem. Phys. (2010), doi:10.1016/j.chemphys.2010.06.010
References in corpus (12)
- Characterizing dynamics with covariant Lyapunov vectors
- Goldstone modes in Lyapunov spectra of hard sphere systems
- Lyapunov instabilities of Lennard-Jones fluids
- Violation of hyperbolicity in a diffusive medium with local hyperbolic attractor
- Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems
- Lyapunov Modes in Hard-Disk Systems
- Stepwise structure of Lyapunov spectra for many particle systems by a random matrix dynamics
- Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
- Lyapunov spectra of periodic orbits for a many-particle system
- Identifying rare chaotic and regular trajectories in dynamical systems with Lyapunov weighted path sampling
- Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems
- Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
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