Scaling behaviour of non-hyperbolic coupled map lattices

dc.creatorGroote, Stefan
dc.creatorBeck, Christian
dc.date2006-03-29
dc.date2006-11-03
dc.date.accessioned2026-07-07T07:07:29Z
dc.date.available2026-07-07T07:07:29Z
dc.descriptionCoupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value. We develop a general 1st order perturbation theory to analytically calculate the invariant 1-point density, show that the density exhibits log-periodic oscillations in phase space, and obtain excellent agreement with numerical results.
dc.description5 pages, including 5 encapsulated PostScript figures
dc.identifierhttps://arxiv.org/abs/nlin/0603067
dc.identifierhttp://arxiv.org/abs/nlin/0603067
dc.identifierPhys. Rev. E74 (2006) 046216
dc.identifierdoi:10.1103/PhysRevE.74.046216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110411
dc.subjectChaotic Dynamics
dc.titleScaling behaviour of non-hyperbolic coupled map lattices
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