Some ergodic properties of the negative slope algorithm

Koshiro Ishimura, Hitoshi Nakada

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2007 Sept
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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