Real Analysis Exchange

Ergodic Properties of Rational Functions that Preserve Lebesgue Measure on ℝ

Rachel L. Bayless

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Abstract

We prove that all negative generalized Boole transformations are conservative, exact, pointwise dual ergodic, and quasi-finite with respect to Lebesgue measure on the real line. We then provide a formula for computing the Krengel, Parry, and Poisson entropy of all conservative rational functions that preserve Lebesgue measure on the real line.

Article information

Source
Real Anal. Exchange, Volume 43, Number 1 (2018), 137-154.

Dates
First available in Project Euclid: 2 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1525226427

Digital Object Identifier
doi:10.14321/realanalexch.43.1.0137

Mathematical Reviews number (MathSciNet)
MR3816436

Zentralblatt MATH identifier
06924878

Subjects
Primary: 37A40: Nonsingular (and infinite-measure preserving) transformations 37A35: Entropy and other invariants, isomorphism, classification

Keywords
entropy infinite measure rational functions generalized Boole\\ transformations

Citation

Bayless, Rachel L. Ergodic Properties of Rational Functions that Preserve Lebesgue Measure on ℝ. Real Anal. Exchange 43 (2018), no. 1, 137--154. doi:10.14321/realanalexch.43.1.0137. https://projecteuclid.org/euclid.rae/1525226427


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