## Osaka Journal of Mathematics

- Osaka J. Math.
- Volume 44, Number 3 (2007), 667-683.

### Some ergodic properties of the negative slope algorithm

Koshiro Ishimura and Hitoshi Nakada

#### 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.

#### Article information

**Source**

Osaka J. Math., Volume 44, Number 3 (2007), 667-683.

**Dates**

First available in Project Euclid: 13 September 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.ojm/1189717427

**Mathematical Reviews number (MathSciNet)**

MR2360945

**Zentralblatt MATH identifier**

1135.11040

**Subjects**

Primary: 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx] 37A05: Measure-preserving transformations 37A25: Ergodicity, mixing, rates of mixing

#### Citation

Ishimura, Koshiro; Nakada, Hitoshi. Some ergodic properties of the negative slope algorithm. Osaka J. Math. 44 (2007), no. 3, 667--683. https://projecteuclid.org/euclid.ojm/1189717427