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Symbol-to-symbol correlation function at the Feigenbaum point of the logistic map

Karamanos, Kostas and Mistakidis, I.S. and Mistakidis, S.I. (2012) Symbol-to-symbol correlation function at the Feigenbaum point of the logistic map. International Journal of Bifurcation and Chaos, 23 (7). ISSN 0218-1274

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    Abstract

    Recently, simple dynamical systems as the 1-d maps on the interval, gained significant attention in the context of statistical physics and complex systems.The decay of correlations in these systems, can be characterized and measured by correlation functions.Thus, in the context of symbolic dynamics of the non-chaotic multifractal attractors (i.e. Feigenbaum attractors), another observable, the symbol-to-symbol correlation function, for the generating partition of the logistic map, is rigorously introduced and checked with numerical experiments. Thanks to the Metropolis-Stein-Stein (MSS) algorithm this observable can be calculated analytically, giving predictions in absolute accordance with numerical computations. The deep, algorithmic structure of the observable is revealed clearly reflecting the complexity of the multifractal attractor.

    Item Type: Article
    Subjects: 37-xx Dynamical systems and ergodic theory
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 23 May 2012 10:04
    Last Modified: 21 Oct 2013 09:29
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/935

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