Convective Lyapunov Spectra

Details Convective Lyapunov Spectra Convective Lyapunov Spectra

2012-01-20

arxiv.org/abs/1201.4346v1

Nonlinear Sciences

Chaotic Dynamics

5 pages, 5 figures, Submitted to Europhysics Letters

Scientific paper

We generalize the concept of convective (or velocity-dependent) Lyapunov exponent $\Lambda(v)$ to an entire spectrum $\Lambda(v,n)$. Our results are supported by the consistency between the outcome of the chronotopic approach [{\it S. Lepri et al. J. Stat. Phys., 82 5/6 (1996) 1429}] and a more direct method. There exists a critical integrated density $n=n_c$, beyond which the convective exponent exhibits a discontinuous dependence on the velocity, which originates from the appearance of multiple branches. This phenomenon can be traced back to a change of concavity of the so-called {\it temporal} Lyapunov spectrum for $n>n_c$, which is therefore a dynamical invariant.

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