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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Publicado: 1995
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v6_nC_p75_Cesaratto
http://hdl.handle.net/20.500.12110/paper_09600779_v6_nC_p75_Cesaratto
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spelling paper:paper_09600779_v6_nC_p75_Cesaratto2023-06-08T15:57:31Z 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 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. 1995 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v6_nC_p75_Cesaratto 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
collection 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.
title Multifractal spectra and hyperbolic geometry
spellingShingle 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
publishDate 1995
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v6_nC_p75_Cesaratto
http://hdl.handle.net/20.500.12110/paper_09600779_v6_nC_p75_Cesaratto
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