Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations

S. Kuznetsov; Andrew Osbaldestin

doi:10.1070/RD2002v007n03ABEH000214

Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations

S. Kuznetsov, Andrew Osbaldestin

School of Mathematics & Physics

Research output: Contribution to journal › Article › peer-review

Abstract

A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations with coefficients expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results depends only on the accuracy of the representation of the universal function.

Original language	English
Pages (from-to)	325
Number of pages	1
Journal	Regular and Chaotic Dynamics
Volume	7
Issue number	3
DOIs	https://doi.org/10.1070/RD2002v007n03ABEH000214
Publication status	Published - 2002

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title = "Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations",

abstract = "A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations with coefficients expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results depends only on the accuracy of the representation of the universal function.",

author = "S. Kuznetsov and Andrew Osbaldestin",

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doi = "10.1070/RD2002v007n03ABEH000214",

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AU - Kuznetsov, S.

AU - Osbaldestin, Andrew

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AB - A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations with coefficients expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results depends only on the accuracy of the representation of the universal function.

U2 - 10.1070/RD2002v007n03ABEH000214

DO - 10.1070/RD2002v007n03ABEH000214

M3 - Article

SN - 1560-3547

VL - 7

SP - 325

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

IS - 3

ER -

Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations

Abstract

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