MULTIFRACTAL SPECTRA AND HYPERBOLIC GEOMETRY

被引:1
|
作者
CESARATTO, E
GRYNBERG, S
HANSEN, R
PIACQUADIO, M
机构
[1] Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, 1428 Capital Federal, Ciudad Universitaria
关键词
D O I
10.1016/0960-0779(95)80013-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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. Tel 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 Poincare circle. In connection with the metrics of the spectral decomposition curves, we derive the same constants obtained in physics.
引用
收藏
页码:75 / 82
页数:8
相关论文
共 50 条
  • [41] On the hyperbolic symplectic geometry
    Gramlich, R
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2004, 105 (01) : 97 - 110
  • [42] Hyperbolic geometry and disks
    Gehring, FW
    Hag, K
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 105 (1-2) : 275 - 284
  • [43] Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra
    Mangalam, Madhur
    Kelty-Stephen, Damian G.
    [J]. PHYSICAL REVIEW E, 2024, 109 (06)
  • [44] Quasi-conformal geometry and hyperbolic geometry
    Bourdon, M
    Pajot, H
    [J]. RIGIDITY IN DYNAMICS AND GEOMETRY: CONTRIBUTIONS FROM THE PROGRAMME ERGODIC THEORY, GEOMETRIC RIGIDITY AND NUMBER THEORY, 2002, : 1 - 17
  • [45] A Characterization of Hyperbolic Geometry among Hilbert Geometry
    Guo, Ren
    [J]. JOURNAL OF GEOMETRY, 2008, 89 (1-2) : 48 - 52
  • [46] Multifractal analysis of non-uniformly hyperbolic systems
    Johansson, Anders
    Jordan, Thomas M.
    Oberg, Anders
    Pollicott, Mark
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 2010, 177 (01) : 125 - 144
  • [47] Multifractal analysis of homological growth rates for hyperbolic surfaces
    Jaerisch, Johannes
    Takahasi, Hiroki
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2024,
  • [48] HYPERBOLIC WAVELET LEADERS FOR ANISOTROPIC MULTIFRACTAL TEXTURE ANALYSIS
    Roux, S. G.
    Abry, P.
    Vedel, B.
    Jaffard, S.
    Wendt, H.
    [J]. 2016 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP), 2016, : 3558 - 3562
  • [49] Multifractal analysis of non-uniformly hyperbolic systems
    Anders Johansson
    Thomas M. Jordan
    Anders Öberg
    Mark Pollicott
    [J]. Israel Journal of Mathematics, 2010, 177 : 125 - 144
  • [50] Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes
    Barreira, Luis
    Iommi, Godofredo
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 2011, 181 (01) : 347 - 379