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 $n\geq 10$. 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.
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2019 ◽
Vol 2019
(748)
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pp. 153-172
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2017 ◽
Vol 29
(06)
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pp. 1750018
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1995 ◽
Vol 04
(02)
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pp. 213-224
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2009 ◽
Vol 30
(2)
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pp. 379-398
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1932 ◽
Vol 18
(12)
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pp. 712-713
2007 ◽
Vol 18
(04)
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pp. 411-453
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2015 ◽
Vol 26
(09)
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pp. 1550066
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2004 ◽
Vol 56
(6)
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pp. 1228-1236
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