Multifractal spectra and hyperbolic geometry
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 consta...
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todo:paper_09600779_v6_nC_p75_Cesaratto2023-10-03T15:53:38Z Multifractal spectra and hyperbolic geometry Cesaratto, E. Grynberg, S. Hansen, R. Piacquadio, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09600779_v6_nC_p75_Cesaratto |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Cesaratto, E. Grynberg, S. Hansen, R. Piacquadio, M. |
| spellingShingle |
Cesaratto, E. Grynberg, S. Hansen, R. Piacquadio, M. Multifractal spectra and hyperbolic geometry |
| author_facet |
Cesaratto, E. Grynberg, S. Hansen, R. Piacquadio, M. |
| author_sort |
Cesaratto, E. |
| title |
Multifractal spectra and hyperbolic geometry |
| title_short |
Multifractal spectra and hyperbolic geometry |
| title_full |
Multifractal spectra and hyperbolic geometry |
| title_fullStr |
Multifractal spectra and hyperbolic geometry |
| title_full_unstemmed |
Multifractal spectra and hyperbolic geometry |
| title_sort |
multifractal spectra and hyperbolic geometry |
| url |
http://hdl.handle.net/20.500.12110/paper_09600779_v6_nC_p75_Cesaratto |
| work_keys_str_mv |
AT cesarattoe multifractalspectraandhyperbolicgeometry AT grynbergs multifractalspectraandhyperbolicgeometry AT hansenr multifractalspectraandhyperbolicgeometry AT piacquadiom multifractalspectraandhyperbolicgeometry |
| _version_ |
1807319385170247680 |