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December 2007 Invariant Measures for a Class of Rational Transformations and Ergodic Properties
Hiroshi ISHITANI, Kensuke ISHITANI
Tokyo J. Math. 30(2): 325-341 (December 2007). DOI: 10.3836/tjm/1202136679

Abstract

This paper is concerned with giving explicitly the invariant density for a class of rational transformations from the real line $\mathbf{R}$ into itself. We proved that the invariant density can be written in terms of the fixed point $z_{0}$ in $\mathbf{C} \setminus \mathbf{R}$ or in terms of the periodic point $z_{0}$ in $\mathbf{C} \setminus \mathbf{R}$ with period 2. The explicit form of the density allows us to obtain the ergodic properties of the transformation $R$.

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Hiroshi ISHITANI. Kensuke ISHITANI. "Invariant Measures for a Class of Rational Transformations and Ergodic Properties." Tokyo J. Math. 30 (2) 325 - 341, December 2007. https://doi.org/10.3836/tjm/1202136679

Information

Published: December 2007
First available in Project Euclid: 4 February 2008

zbMATH: 1145.37001
MathSciNet: MR2376512
Digital Object Identifier: 10.3836/tjm/1202136679

Subjects:
Primary: 37A05
Secondary: 37A50, 60F05

Rights: Copyright © 2007 Publication Committee for the Tokyo Journal of Mathematics

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Vol.30 • No. 2 • December 2007
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