Lacunarity and Period-doubling

Glendinning, Paul and Smith, Leonard A. (2012) Lacunarity and Period-doubling. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Additional Information: CICADA
Uncontrolled Keywords: lacunarity, fractal, period-doubling, universality class
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
Depositing User: Professor Paul Glendinning
Date Deposited: 03 Aug 2012
Last Modified: 08 Nov 2017 18:18

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