Let Mod ( S ) Mod(S) upper M o d left parenthesis upper S right parenthesis be the mapping class group of a closed orientable surface S of genus g ≥ 2 g ≥ 2 g greater than or equals 2 . Let G be a non-elementary subgroup of Mod ( S ) Mod(S) upper M o d left parenthesis upper S right parenthesis such that the associated Bowen–Margulis measure is finite. In this paper, we give an asymptotic growth formula for G with respect to the Teichmüller metric.
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Gekhtman et al. (2026) studied this question.
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