Microcanonical multifractal formalism -: a geometrical approach to multifractal systems:: Part I.: Singularity analysis

被引：77
作者：
Turiel, Antonio [1 ]
Yahia, Hussein [2 ]
Perez-Vicente, Conrad J. [3 ]
机构：
[1] CSIC, Inst Ciencies Mar, E-08003 Barcelona, Spain
[2] INRIA Roquencourt, Clime Project, F-78153 Le Chesnay, France
[3] Univ Barcelona, Dept Fis Fonamental, E-08028 Barcelona, Spain
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2008年 / 41卷 / 01期
关键词：
D O I：
10.1088/1751-8113/41/1/015501
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals, typically associated with natural phenomena in scale invariant systems. In this paper, we discuss the multifractal microcanonical formalism in a comprehensive, unified way, including new theoretical proofs and validation tests on real signals, so completing some known gaps in the foundations of this theory. We also review the latest advances and describe the present perspectives in this field. Some technical details on the implementation of involved algorithms and relevant open issues are also discussed.
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页数：35
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