Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

Details Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

2010-08-30

arxiv.org/abs/1008.5186v2

Phys. Rev. E 82, 036205 (2010) [6 pages]

Nonlinear Sciences

Chaotic Dynamics

7 pages, 5 figures

Scientific paper

10.1103/PhysRevE.82.036205

In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and $\Phi^4$ models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a `bit reversible' algorithm, which completely obviates computer memory limitations.

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