An implementation of the Bestvina-Handel algorithm for surface homeomorphisms. (English) Zbl 0982.57005

Brinkmann, Peter

Exp. Math. 9, No. 2, 235-240 (2000).

Summary: M. Bestvina and M. Handel [Topology 34, No. 1, 109-140 (1995; Zbl 0837.57010)] have introduced an effective algorithm that determines whether a given homeomorphism of an orientable, possibly punctured surface is pseudo-Anosov. We present a Java software package that realizes this algorithm for surfaces with one puncture. It allows the user to define homeomorphisms in terms of Dehn twists, and in the pseudo-Anosov case it generates images of train tracks in the sense of Bestvina-Handel.

MSC:

57M60	Group actions on manifolds and cell complexes in low dimensions
37E30	Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37D20	Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
57-04	Software, source code, etc. for problems pertaining to manifolds and cell complexes

Keywords:

pseudo-Anosov; train tracks

Citations:

Zbl 0837.57010

References:

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