Artículo
Abstract:
In recent years Procaccia, Kohmoto, and others studied non-regular fractal sets appearing in physics -such as the strange attractors- using the multifractal spectral decomposition technique introduced by Procaccia. These studies allowed the discovery of the so-called universal functions - and constants. Thus, a number of apparently unconnected physical phenomena have associated fractal sets with the same spectral decomposition function. Tél proposed a qualitative, tentative classification of the universal functions known so far. We model these using hyperbolic geometry, by decomposing the limit sets of finitely generated groups of motions in the Poincarécircle. In connection with the metrics of the spectral decomposition curves, we dérive the same constants obtained in physics. © 1995 Elsevier Science Ltd.
Registro:
| Documento: | Artículo |
| Título: | Multifractal spectra and hyperbolic geometry |
| Autor: | Cesaratto, E.; Grynberg, S.; Hansen, R.; Piacquadio, M. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Capital Federal, Argentina |
| Año: | 1995 |
| Volumen: | 6 |
| Número: | C |
| Página de inicio: | 75 |
| Página de fin: | 82 |
| DOI: | http://dx.doi.org/10.1016/0960-0779(95)80013-7 |
| Título revista: | Chaos, Solitons and Fractals |
| Título revista abreviado: | Chaos Solitons Fractals |
| ISSN: | 09600779 |
| CODEN: | CSFOE |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v6_nC_p75_Cesaratto |
Referencias:
- Halsey, Jensen, Kadanoff, Procaccia, Shraiman, Fractal measures and their singularities: the characterization of strange sets (1987) Nuclear Physics B (Proc. Suppl.), 2, pp. 501-512
- Duong-van, Phase transition of multifractals (1987) Nuclear Physics B (Proc. Suppl.), 2, pp. 521-526
- Jensen, Kadanoff, Libchaber, Procaccia, Stavans, Global universality at the onset of chaos: results of a forced Rayleigh-Bénard experiment (1987) Nuclear Physics B (Proc. Suppl.), 2, pp. 513-516
- Cvitanovic, Jensen, Kadanoff, Procaccia, Renormalization, unstable manifolds, and the fractal structure of mode locking (1985) Physical Review Letters, 55 (4), pp. 343-346
- Bak, The Devil's staircase (1986) Physics Today, pp. 38-45
- Kohmoto, Sutherland, Electronic states on a Penrose lattice (1986) Physical Review Letters, 56 (25), pp. 2740-2743
- Tél, Fractals, multifractals and thermodynamics (1988) Z. Naturforsch, 43 a, pp. 1154-1174
- Gumbs, Ali, Electronic properties of the tight binding Fibonacci Hamiltonian (1989) J. Physics A. Math. Gen., 22, pp. 951-970
- S. Grynberg and M. Piacquadio, Hyperbolic geometry and multifractal spectra, Preprint book, Deparment of Mathematics, University of Buenos Aires (in press)
Citas:
---------- APA ----------
Cesaratto, E., Grynberg, S., Hansen, R. & Piacquadio, M. (1995) . Multifractal spectra and hyperbolic geometry. Chaos, Solitons and Fractals, 6(C), 75-82.http://dx.doi.org/10.1016/0960-0779(95)80013-7
---------- CHICAGO ----------
Cesaratto, E., Grynberg, S., Hansen, R., Piacquadio, M. "Multifractal spectra and hyperbolic geometry" . Chaos, Solitons and Fractals 6, no. C (1995) : 75-82.http://dx.doi.org/10.1016/0960-0779(95)80013-7
---------- MLA ----------
Cesaratto, E., Grynberg, S., Hansen, R., Piacquadio, M. "Multifractal spectra and hyperbolic geometry" . Chaos, Solitons and Fractals, vol. 6, no. C, 1995, pp. 75-82.http://dx.doi.org/10.1016/0960-0779(95)80013-7
---------- VANCOUVER ----------
Cesaratto, E., Grynberg, S., Hansen, R., Piacquadio, M. Multifractal spectra and hyperbolic geometry. Chaos Solitons Fractals. 1995;6(C):75-82.http://dx.doi.org/10.1016/0960-0779(95)80013-7
