Real Analysis Exchange

Ergodic Properties of Rational Functions that Preserve Lebesgue Measure on ℝ

Rachel L. Bayless

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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

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

First available in Project Euclid: 2 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

entropy infinite measure rational functions generalized Boole\\ transformations


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.

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