Lacunarity and period-doubling

Paul Glendinning; Leonard A. Smith

doi:10.1080/14689367.2012.755496

Lacunarity and period-doubling

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Abstract

We show that the deviation from power laws of the scaling of chaotic measures, such as Lyapunov exponents and topological entropy, is periodic in the logarithm of the distance from the accumulation of period doubling. Moreover, this periodic function is asymptotically universal for each measure (for functions in the appropriate universality class). This is related to the concept of lacunarity known to exist for scaling functions describing the mass distribution of self-similar fractal sets. © 2013 Copyright Taylor and Francis Group, LLC.

Original language	English
Pages (from-to)	111-121
Number of pages	10
Journal	Dynamical Systems: an international journal
Volume	28
Issue number	1
DOIs	https://doi.org/10.1080/14689367.2012.755496
Publication status	Published - 1 Mar 2013

Keywords

fractal
lacunarity
period-doubling
universality class

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10.1080/14689367.2012.755496

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AB - We show that the deviation from power laws of the scaling of chaotic measures, such as Lyapunov exponents and topological entropy, is periodic in the logarithm of the distance from the accumulation of period doubling. Moreover, this periodic function is asymptotically universal for each measure (for functions in the appropriate universality class). This is related to the concept of lacunarity known to exist for scaling functions describing the mass distribution of self-similar fractal sets. © 2013 Copyright Taylor and Francis Group, LLC.

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KW - period-doubling

KW - universality class

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Lacunarity and period-doubling

Abstract

Keywords

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