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Title: Universality of the route to chaos: Exact analysis
Authors: Okubo, Ken-ichi
Umeno, Ken  kyouindb  KAKEN_id
Author's alias: 大久保, 健一
梅野, 健
Issue Date: Oct-2018
Publisher: Oxford University Press (OUP)
Journal title: Progress of Theoretical and Experimental Physics
Volume: 2018
Issue: 10
Thesis number: 103A01
Abstract: The universality of the route to chaos is analytically proven for a countably infinite number of maps by proposing Super Generalized Boole (SGB) transformations. One of the routes to chaos, the intermittency route, was previously studied extensively by numerical methods. These researchers conjectured the universality in Type 1 intermittency, namely that the critical exponent of the Lyapunov exponent in this type of intermittency is 1/2. We prove their conjecture by showing that, for certain parameter ranges, the SGB transformations are exact and preserve the Cauchy distribution. Using the property of exactness, we prove that the critical exponent is 1/2 for a countably infinite number of maps where Type 1 intermittency occurs.
Rights: © The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
DOI(Published Version): 10.1093/ptep/pty094
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