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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

Abstract

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.

Information

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

zbMATH: 1187.37046
MathSciNet: MR2582409

Digital Object Identifier: 10.2969/aspm/05310095

Rights: Copyright © 2009 Mathematical Society of Japan

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