Scaling behaviour of non-hyperbolic coupled map lattices
| dc.creator | Groote, Stefan | |
| dc.creator | Beck, Christian | |
| dc.date | 2006-03-29 | |
| dc.date | 2006-11-03 | |
| dc.date.accessioned | 2026-07-07T07:07:29Z | |
| dc.date.available | 2026-07-07T07:07:29Z | |
| dc.description | Coupled 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.description | 5 pages, including 5 encapsulated PostScript figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0603067 | |
| dc.identifier | http://arxiv.org/abs/nlin/0603067 | |
| dc.identifier | Phys. Rev. E74 (2006) 046216 | |
| dc.identifier | doi:10.1103/PhysRevE.74.046216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110411 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Scaling behaviour of non-hyperbolic coupled map lattices | |
| dc.type | text |