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Complexity and Unpredictable Scaling of Hierarchical Structures

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Chaotic Dynamics

Part of the book series: NATO ASI Series ((NSSB,volume 298))

Abstract

The problem of characterizing complexity is formulated in the framework of a hierarchical modelling of physical systems. Complexity is related to the task of predicting the asymptotic scaling behaviour of system’s observables from the available finite-resolution measurements. The analysis is performed on one-dimensional stationary symbolic patterns such as those encountered in nonlinear dynamics, cellular automata, spin systems, making use of suitable coding methods in a statistical-mechanical environment. The asymptotic limit of thermodynamic sums is estimated within a grand-canonical formalism, with the help of transfer-matrix and renormalization techniques: the convergence of the associated scaling functions is directly related to the previously defined complexity measure.

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Authors and Affiliations

  1. Paul Scherrer Institute, LUS, CH-5232, Villigen PSI, Switzerland

    R. Badii

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  1. R. Badii
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  1. University of Patras, Patras, Greece

    T. Bountis

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© 1992 Springer Science+Business Media New York

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Badii, R. (1992). Complexity and Unpredictable Scaling of Hierarchical Structures. In: Bountis, T. (eds) Chaotic Dynamics. NATO ASI Series, vol 298. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3464-8_1

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  • DOI: https://doi.org/10.1007/978-1-4615-3464-8_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6534-1

  • Online ISBN: 978-1-4615-3464-8

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