Pseudo-Anosov maps with small stretch factors on punctured surfaces

Abstract

Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus $g$ with $n$ punctures. We determine the behaviour of this minimum number for a certain large subset of the $(g,n)$ plane, up to a multiplicative constant. In particular it has been shown that for fixed $n$, this minimum value behaves as $\frac{1}{g}$, proving what Penner speculated in 1991.

To appear in Algebraic & Geometric Topology, 26 pages, 10 figures

References in corpus (6)

• A family of pseudo-Anosov braids with small dilatation
• Lower bound for the Perron-Frobenius degrees of Perron numbers
• Minimal pseudo-Anosov stretch factors on nonoriented surfaces
• Minimal Penner dilatations on nonorientable surfaces
• Minimal dilatation in Penner's construction
• Least dilatation of pure surface braids

Cited by in corpus (1)

• Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor