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تسجيل مستخدم جديدCounting Conjugacy Classes in $Out(F_N)$
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We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $Nge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully irreducibles $phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with $loglambda(phi)$ on the order of $R$ grows exponentially in $R$.
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