Scaling properties of invariant densities of coupled Tchebyscheff maps
| dc.creator | Groote, Stefan | |
| dc.creator | Beck, Christian | |
| dc.date | 2006-09-21 | |
| dc.date | 2008-06-23 | |
| dc.date.accessioned | 2026-07-07T09:45:57Z | |
| dc.date.available | 2026-07-07T09:45:57Z | |
| dc.description | We study 1-dimensional coupled map lattices consisting of diffusively coupled Tchebyscheff maps of N-th order. For small coupling constants a we determine the invariant 1-point and 2-point densities of these nonhyperbolic systems in a perturbative way. For arbitrarily small couplings a>0 the densities exhibit a selfsimilar cascade of patterns, which we analyse in detail. We prove that there are log-periodic oscillations of the density both in phase space as well as in parameter space. We show that expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the case of hyperbolic maps where one has scaling with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of the expectation value of any given observable. | |
| dc.description | 31 pages, including 19 encapsulated PostScript figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0609052 | |
| dc.identifier | http://arxiv.org/abs/nlin/0609052 | |
| dc.identifier | Dyn. Sys. 22(2) (2007) 219-248 | |
| dc.identifier | doi:10.1080/14689360601173385 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163366 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Scaling properties of invariant densities of coupled Tchebyscheff maps | |
| dc.type | text |