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On the Characterization of Chaotic Systems Using Multifractals

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Time-Dependent Effects in Disordered Materials

Part of the book series: NATO ASI Series ((ASIB,volume 167))

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Abstract

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.

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References

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Author information

Authors and Affiliations

  1. NORDITA, Blegdamsvej, 17, DK-2100, Copenhagen, Denmark

    Vicent J. Martínez

Authors
  1. Vicent J. Martínez
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Editor information

Editors and Affiliations

  1. LANSCE MS-H805, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Roger Pynn (director) (director)

  2. Institute for Energy Technology, POB 40, N-2007, Kjeller, Norway

    Tormod Riste (co-director) (co-director)

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© 1987 Plenum Press, New York

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Martínez, V.J. (1987). On the Characterization of Chaotic Systems Using Multifractals. In: Pynn, R., Riste, T. (eds) Time-Dependent Effects in Disordered Materials. NATO ASI Series, vol 167. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7476-3_16

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  • DOI: https://doi.org/10.1007/978-1-4684-7476-3_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-7478-7

  • Online ISBN: 978-1-4684-7476-3

  • eBook Packages: Springer Book Archive

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