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ID 116701
Author
Miino, Yuu Tokyo University of Technology
Keywords
two-to-one map
unstable periodic point
symbolic dynamical system
Content Type
Journal Article
Description
In this study, we have focused on the two-to-one maps and developed the numerical method to calculate the unstable periodic points (UPPs), based on the theory of the symbolic dynamical system. The core technique of the method is the definition of a non-deterministic map G. From the experimental result of three typical maps: logistic map, tent map, and Bernoulli map, we have confirmed the proposed method works very well within the defined errors. Our method has the following advantages: the method converges rapidly as the period of the target UPP is larger; we can choose the target UPP regardless of its cause (any bifurcation is not a matter); we can find the UPPs that are always unstable in the given parameter range. The convergence of the method is guaranteed by two standpoints: the corresponding symbolic dynamical system, and the asymptotic stability of UPP of G. Hereby, the error of the convergence is scalable according to the numeric precision of the software.
Journal Title
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
Publisher
The Institute of Electronics, Information and Communication Engineers
Volume
13
Issue
2
Start Page
215
End Page
220
Published Date
2022-04-01
Rights
©IEICE 2022
EDB ID
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Publisher
departments
Center for Administration of Information Technology