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| Titel: |
Scaling properties of invariant densities of coupled Chebyshev maps |
| Auteur: |
Groote, Stefan Beck, Christian |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 22 (2007) nr. 2 pagina's 219-248 |
| Jaar: |
2007-06 |
| Inhoud: |
We study one-dimensional coupled map lattices consisting of diffusively coupled Chebyshev 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 [image omitted] 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 N2 modulating the [image omitted]-dependence of the expectation value of any given observable. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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