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On the angle between the first and second Lyapunov vectors in spatio-temporal chaos

AuthorsPazó, Diego ; López, Juan M. ; Rodríguez, Miguel A.
Issue Date2013
PublisherInstitute of Physics Publishing
CitationJournal of Physics A: Mathematical and Theoretical 46(25): 254014 (2013)
AbstractIn a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates - at any point on the attractor - the direction of maximal growth in tangent space. The LV corresponding to the second largest Lyapunov exponent generally points in a different direction, but tangencies between both vectors can in principle occur. Here we find that the probability density function (PDF) of the angle ψ spanned by the first and second LVs should be expected to be approximately symmetric around π/4 and to peak at 0 and π/2. Moreover, for small angles we uncover a scaling law for the PDF Q of ψl = ln ψ with the system size L: Q(ψl) = L -1/2f(ψlL-1/2). We give a theoretical argument that justifies this scaling form and also explains why it should be universal (irrespective of the system details) for spatio-temporal chaos in one spatial dimension.
Identifiersdoi: 10.1088/1751-8113/46/25/254014
issn: 1751-8113
e-issn: 1751-8121
Appears in Collections:(IFCA) Artículos
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