Tokyo Journal of Mathematics

Invariant Measures for a Class of Rational Transformations and Ergodic Properties

Hiroshi ISHITANI and Kensuke ISHITANI

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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 $R$.

Article information

Source
Tokyo J. Math., Volume 30, Number 2 (2007), 325-341.

Dates
First available in Project Euclid: 4 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1202136679

Digital Object Identifier
doi:10.3836/tjm/1202136679

Mathematical Reviews number (MathSciNet)
MR2376512

Zentralblatt MATH identifier
1145.37001

Subjects
Primary: 37A05: Measure-preserving transformations
Secondary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60F05: Central limit and other weak theorems

Citation

ISHITANI, Hiroshi; ISHITANI, Kensuke. Invariant Measures for a Class of Rational Transformations and Ergodic Properties. Tokyo J. Math. 30 (2007), no. 2, 325--341. doi:10.3836/tjm/1202136679. https://projecteuclid.org/euclid.tjm/1202136679


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