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September 2007 Some ergodic properties of the negative slope algorithm
Koshiro Ishimura, Hitoshi Nakada
Osaka J. Math. 44(3): 667-683 (September 2007).


The notion of the negative slope algorithm was introduced by S. Ferenczi, C. Holton, and L. Zamboni as an induction process of three interval exchange transformations. Then S. Ferenczi and L.F.C. da Rocha gave the explicit form of its absolutely continuous invariant measure and showed that it is ergodic. In this paper we prove that the negative slope algorithm with the absolutely continuous invariant measure is weak Bernoulli. We also show that this measure is derived as a marginal distribution of an invariant measure for a 4-dimensional (natural) extension of the negative slope algorithm. We also calculate its entropy by Rohlin's formula.


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Koshiro Ishimura. Hitoshi Nakada. "Some ergodic properties of the negative slope algorithm." Osaka J. Math. 44 (3) 667 - 683, September 2007.


Published: September 2007
First available in Project Euclid: 13 September 2007

zbMATH: 1135.11040
MathSciNet: MR2360945

Primary: 11K55, 37A05, 37A25

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics


Vol.44 • No. 3 • September 2007
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