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Nonlinear Sciences > Chaotic Dynamics

arXiv:1404.7774 (nlin)
[Submitted on 30 Apr 2014]

Title:Knotted Strange Attractors and Matrix Lorenz Systems

Authors:J. Tranchida, P. Thibaudeau, S. Nicolis
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Abstract:A generalization of the Lorenz equations is proposed where the variables take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of $\mathfrak{u}(2)$. We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.
Comments: 10 pages Revtex, 3 figures
Subjects: Chaotic Dynamics (nlin.CD); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)
Cite as: arXiv:1404.7774 [nlin.CD]
  (or arXiv:1404.7774v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.1404.7774

Submission history

From: Stam Nicolis [view email]
[v1] Wed, 30 Apr 2014 16:05:32 UTC (1,868 KB)
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