On the Characterization of Chaotic Systems Using Multifractals

  • Vicent J. Martínez
Part of the NATO ASI Series book series (volume 167)


A dynamical system is a set of differential equations describing the time evolution of a physical system which initial conditions are knowed. The solution of the system is a trajectory in phase space (each point of this trajectory represents a state of motion of the system). Systems can be conservative, when they preserve the volume in phase space, and also dissipative, if that volume is shrinked continuously. However it is possible to observe chaotic or stochastic motions in both cases, but it is not clear how to characterize globally the stochasticity or how to measure the randomness. In this paper we apply the multifractal formalism and in particular the f(α) spectrum of singularities1 in order to characterize both kinds of systems.


Probability Measure Fractal Dimension Chaotic System Hausdorff Dimension Temporal Probability 
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  1. 1.
    T.C. Hasley, M.H. Jensen, L.P. Kadanoff, I. Procaccia and B.I. Shraiman, Phys. Rev. A33, 1141 (1986)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    M.H. Jensen, L.P. Kadanoff, A. Libchaber, I. Procaccia and J. Stavans, Phys. Rev. Lett. 55, 2798 (1985)ADSCrossRefGoogle Scholar
  3. 3.
    H.G.E. Hentschel and I. Procaccia, Physica 8D, 435 (1983)MathSciNetMATHGoogle Scholar
  4. 4.
    M. Hénon, Commun. Math. Phys. 50, 69 (1976)ADSMATHCrossRefGoogle Scholar
  5. 5.
    M. Hénon and C. Heiles, Astron.-J. 73, 964 (1969)Google Scholar
  6. 6.
    C.M. Bender and S.A. Orszag, “Advanced Mathematical Methods for Scientist and Engineers”. McGrawll-Hill, (1978)Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Vicent J. Martínez
    • 1
  1. 1.NORDITACopenhagenDenmark

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