### 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 1 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Some ergodic properties of the negative slope algorithm'. Together they form a unique fingerprint.

## Cite this

Ishimura, K., & Nakada, H. (2007). Some ergodic properties of the negative slope algorithm.

*Osaka Journal of Mathematics*,*44*(3), 667-683.