Some ergodic properties of the negative slope algorithm

Koshiro Ishimura, Hitoshi Nakada

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)667-683
Number of pages17
JournalOsaka Journal of Mathematics
Volume44
Issue number3
Publication statusPublished - 2007 Sep

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Absolutely Continuous Invariant Measure
Slope
Interval Exchange Transformation
Natural Extension
Marginal Distribution
Bernoulli
Invariant Measure
Proof by induction
Entropy
Calculate
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Some ergodic properties of the negative slope algorithm. / Ishimura, Koshiro; Nakada, Hitoshi.

In: Osaka Journal of Mathematics, Vol. 44, No. 3, 09.2007, p. 667-683.

Research output: Contribution to journalArticle

Ishimura, K & Nakada, H 2007, 'Some ergodic properties of the negative slope algorithm', Osaka Journal of Mathematics, vol. 44, no. 3, pp. 667-683.
Ishimura, Koshiro ; Nakada, Hitoshi. / Some ergodic properties of the negative slope algorithm. In: Osaka Journal of Mathematics. 2007 ; Vol. 44, No. 3. pp. 667-683.
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