## Experimental Mathematics

- Experiment. Math.
- Volume 16, Issue 2 (2007), 167-180.

### The Minimum Dilatation of Pseudo-Ansonov 5-Braids

Ji-Young Ham and Won Taek Song

#### Abstract

The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero $\lambda_5 \approx 1.72208$ of $x^4 - x^3 - x^2 - x + 1$, which is attained by $\sigma_1\sigma_2\sigma_3\sigma_4\sigma_1\sigma_2$.

#### Article information

**Source**

Experiment. Math., Volume 16, Issue 2 (2007), 167-180.

**Dates**

First available in Project Euclid: 7 March 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1204905873

**Mathematical Reviews number (MathSciNet)**

MR2339273

**Zentralblatt MATH identifier**

1151.37037

**Subjects**

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

Secondary: 37B40: Topological entropy 57M60: Group actions in low dimensions

**Keywords**

Dilation train track braid

#### Citation

Ham, Ji-Young; Song, Won Taek. The Minimum Dilatation of Pseudo-Ansonov 5-Braids. Experiment. Math. 16 (2007), no. 2, 167--180. https://projecteuclid.org/euclid.em/1204905873