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

Antonio Turiel (1) , Hussein Yahia (2) , Conrad J. Perez-Vicente (3)

1 ICM - Institute of Marine Sciences / Institut de Ciències del Mar [Barcelona]
2 GeoStat - Geometry and Statistics in acquisition data
3 UB - Universitat de Barcelona

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.

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Dynamique Chaotique [nlin.CD]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Antonio Turiel, Hussein Yahia, Conrad J. Perez-Vicente. Microcanonical multifractal formalism--a geometrical approach to multifractal systems: Part I. Singularity analysis. Journal of Physics A: Mathematical and Theoretical, 2008, Journal of Physics A: Mathematical and Theoretical, 41, pp.015501-015536. ⟨10.1088/1751-8113/41/1/015501⟩. ⟨hal-00937370⟩