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VOL. 53 | 2009 3-dimensional i.i.d. binary random vectors governed by Jacobian elliptic space curve dynamics
Tohru Kohda

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose


Sufficient conditions have been recently given for a class of ergodic maps of an interval onto itself: $I= [0, 1] \subset R \to I$ and its associated binary function to generate a sequence of independent and identically distributed (i.i.d.) binary random variables. Jacobian elliptic Chebyshev map, its derivative and second derivative induce Jacobian elliptic space curve. A mapping of the space curve with its coordinates, e.g., $X$, $Y$ and $Z$, onto itself is introduced which defines 3 projective onto mappings, represented in the form of rational functions of $\{x_n, y_n, z_n\}_{n=0}^{\infty}$. Such mappings with their absolutely continuous invariant measures as functions of elliptic integrals and their associated binary function can generate a 3-dimensional sequence of i.i.d. binary random vectors.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1187.37046
MathSciNet: MR2582409

Digital Object Identifier: 10.2969/aspm/05310095

Keywords: Bernoulli shift , chaos , coin tossing , duplication formula , elliptic integral , ellpitic space curve , independence , independent and identically distributed binary random variable , Jacobian elliptic function , pseudo-radom number

Rights: Copyright © 2009 Mathematical Society of Japan


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