Entropie topologique et représentation de Burau. (Topological entropy and Burau representation). (French) Zbl 0688.58021

Kolev, Boris

C. R. Acad. Sci., Paris, Sér. I 309, No. 13, 835-838 (1989).

Summary: Let f be an orientation preserving homeomorphism of the disk \(D^ 2\), P a finite invariant set and [f] the isotopy class of f in \(D^ 2-P\). We give a nontrivial minoration of the topological entropy for maps in [f], using the spectral radius of some specializations in GL(n,\({\mathbb{C}})\) of the Burau matrix associated with [f] and we give an example which shows the interest of this minoration.

MSC:

37A99

Ergodic theory

Keywords:

topological entropy; Burau representation