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Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences

Author

Listed:
  • Arneodo, A.
  • Audit, B.
  • Bacry, E.
  • Manneville, S.
  • Muzy, J.F.
  • Roux, S.G.

Abstract

We use the continuous wavelet transform to generalize the multifractal formalism to fractal functions. We report the results of recent applications of the so-called wavelet transform modulus maxima (WTMM) method to fully developed turbulence data and DNA sequences. We conclude by briefly describing some works currently under progress, which are likely to be the guidelines for future research.

Suggested Citation

  • Arneodo, A. & Audit, B. & Bacry, E. & Manneville, S. & Muzy, J.F. & Roux, S.G., 1998. "Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 24-45.
    • Handle: RePEc:eee:phsmap:v:254:y:1998:i:1:p:24-45
    DOI: 10.1016/S0378-4371(98)00002-8
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    Cited by:

    1. Bruni, V. & Canditiis, D.De & Vitulano, D., 2012. "Time-scale energy based analysis of contours of real-world shapes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(12), pages 2891-2907.
    2. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2013. "Multifractality and long memory of a financial index," Papers 1306.0490, arXiv.org.
    3. Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
    4. Mehmet Ali Balcı & Larissa M. Batrancea & Ömer Akgüller & Lucian Gaban & Mircea-Iosif Rus & Horia Tulai, 2022. "Fractality of Borsa Istanbul during the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(14), pages 1-33, July.

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