### 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 language | English |
---|---|

Pages (from-to) | 667-683 |

Number of pages | 17 |

Journal | Osaka Journal of Mathematics |

Volume | 44 |

Issue number | 3 |

Publication status | Published - 2007 Sep |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Osaka Journal of Mathematics*,

*44*(3), 667-683.

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

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 44, no. 3, pp. 667-683.

}

TY - JOUR

T1 - Some ergodic properties of the negative slope algorithm

AU - Ishimura, Koshiro

AU - Nakada, Hitoshi

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36649005733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36649005733&partnerID=8YFLogxK

M3 - Article

VL - 44

SP - 667

EP - 683

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 3

ER -