Is a typical bi-Perron algebraic unit a pseudo-Anosov dilatation?

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In this note, we deduce a partial answer to the question in the title. In particular, we show that asymptotically almost all bi-Perron algebraic units whose characteristic polynomial has degree at most 2n do not correspond to dilatations of pseudo-Anosov maps on a closed orientable surface of genus n for n >= 10. As an application of the argument, we also obtain a statement on the number of closed geodesics of the same length in the moduli space of area-one abelian differentials for low-genus cases.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2019-07
Language
English
Article Type
Article
Citation

ERGODIC THEORY AND DYNAMICAL SYSTEMS, v.39, pp.1745 - 1750

ISSN
0143-3857
DOI
10.1017/etds.2017.109
URI
http://hdl.handle.net/10203/262801
Appears in Collection
MA-Journal Papers(저널논문)
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