New York Journal of Mathematics
Volume 18 (2012) 609-620


Aaron D. Valdivia

Sequences of pseudo-Anosov mapping classes and their asymptotic behavior

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Published: August 15, 2012
Keywords: Mapping class group, pseudo-Anosov, minimal dilatation
Subject: 57M50

In this paper we provide a construction which produces sequences of pseudo-Anosov mapping classes on surfaces with decreasing Euler characteristic. The construction is based on Penner's examples used in the proof that the minimal dilatation, δg,0, for a closed surface of genus g behaves asymptotically like (1/g). We give a bound for the dilatation of the pseudo-Anosov elements of each sequence produced by the construction and use this bound to show that if gi=rni for some rational number r>0 then δgi,ni behaves like (1/|ϗ(Sgi,ni)|) where ϗ(Sgi,ni) is the Euler characteristic of the genus gi surface with ni punctures.

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