ar X iv : 0 70 5 . 38 12 v 2 [ m at h . D S ] 2 4 Ja n 20 08 DYNAMICS OF THE TEICHMÜLLER FLOW ON COMPACT INVARIANT SETS
نویسنده
چکیده
Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is the supremum of the topological entropies of the restriction of Φ t to compact invariant subsets of Q(S).
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ar X iv : 0 70 5 . 38 12 v 1 [ m at h . D S ] 2 5 M ay 2 00 7 DYNAMICS OF THE TEICHMÜLLER FLOW ON COMPACT INVARIANT SETS
Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is...
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