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Structure of the correlation function at the accumulation points of the logistic map

Karamanos, Kostas and Mistakidis, I.S. and Mistakidis, S.I. (2013) Structure of the correlation function at the accumulation points of the logistic map. Communications in Nonlinear Science and Numerical Simulation . (Submitted)

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    Abstract

    The correlation function of the trajectory at the Feigenbaum attractors of the logistic map is rigorously introduced and checked by numerical experiments. Taking advantage of recent closed analytical results on the symbol-to-symbol correlation function, we are in position to justify the deep algorithmic structure of the correlation function apart from numerical constants. A generalization is given for arbitrary $m \cdot 2^\infty$ Feigenbaum attractors.

    Item Type: Article
    Uncontrolled Keywords: Correlation function; Symbolic dynamics; Bifurcation points; Feigenbaum attractors; Logistic map
    Subjects: 37-xx Dynamical systems and ergodic theory
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 26 Apr 2013 11:52
    Last Modified: 26 Apr 2013 11:52
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1470

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