Distribution Phenomena in Continued Fractions and Logistic Map | Zendy

Shuji Obata | Zendy; Shigeru Ohkuro | Zendy

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Distribution Phenomena in Continued Fractions and Logistic Map

Author(s) -

Shuji Obata,

Shigeru Ohkuro

Publication year - 1999

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.101.831

Subject(s) - cauchy distribution , logistic map , physics , statistical physics , tangent , chaotic , distribution (mathematics) , probability distribution , chaos (operating system) , markov chain , probability density function , mathematical analysis , statistics , mathematics , geometry , artificial intelligence , computer science , computer security

We have been studying chaotic behavior and chaos-like behavior in continued fractions. In this paper, such chaos-like behavior is investigated in detail. This behavior originates in the complex numbers that determine the Cauchy distributions, where cyclic terms discretely appear at isolated parameter values. The distributions are formed along with alternate tangent functions that are dominated by the cyclic terms characterized by double-Markov processes. Finally, the probability densities of the logistic map are analyzed based on the Cauchy distributions, like state density calculations in solids.

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