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Periodic orbits in the thin part of strata

  • Ursula Hamenstädt EMAIL logo
Published/Copyright: February 20, 2024
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Journal für die reine und angewandte Mathematik (Crelles Journal)
From the journal Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2024 Issue 809

Abstract

Let S be a closed oriented surface of genus g ≥ 0 with n ≥ 0 punctures and 3 ⁢ g - 3 + n ≥ 5 . Let 𝒬 be a connected component of a stratum in the moduli space 𝒬 ⁢ ( S ) of area one meromorphic quadratic differentials on S with n simple poles at the punctures or in the moduli space ℋ ⁢ ( S ) of abelian differentials on S if n = 0 . For a compact subset K of 𝒬 ⁢ ( S ) or of ℋ ⁢ ( S ) , we show that the asymptotic growth rate of the number of periodic orbits for the Teichmüller flow Φ t on 𝒬 which are entirely contained in 𝒬 - K is at least h ⁢ ( 𝒬 ) - 1 , where h ⁢ ( 𝒬 ) > 0 is the complex dimension of ℝ + ⁢ 𝒬 .

Acknowledgements

A major part of this work was carried out in spring 2010 during a special semester at the Hausdorff Institute for Mathematics in Bonn and in spring 2011 during a visit of the MSRI in Berkeley. I thank both institutes for their hospitality and for the excellent working conditions.

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Received: 2022-10-04
Revised: 2023-11-17
Published Online: 2024-02-20
Published in Print: 2024-04-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Logarithmic Gromov–Witten theory and double ramification cycles
  3. Periodic orbits in the thin part of strata
  4. Deformation theory of cohomological field theories
  5. Moduli spaces of sheaves via affine Grassmannians
  6. Khovanov homology and exotic surfaces in the 4-ball
  7. Ergodic states on type III1 factors and ergodic actions
  8. A matrix version of the Steinitz lemma
  9. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
https://doi.org/10.1515/crelle-2023-0102

Articles in the same Issue

  1. Frontmatter
  2. Logarithmic Gromov–Witten theory and double ramification cycles
  3. Periodic orbits in the thin part of strata
  4. Deformation theory of cohomological field theories
  5. Moduli spaces of sheaves via affine Grassmannians
  6. Khovanov homology and exotic surfaces in the 4-ball
  7. Ergodic states on type III1 factors and ergodic actions
  8. A matrix version of the Steinitz lemma
  9. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
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