Symbolic dynamics for the Teichmueller flow
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2011
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| _version_ | 1866909576786345984 |
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| author | Hamenstädt, Ursula |
| author_facet | Hamenstädt, Ursula |
| contents | Let Q be a component of a stratum of abelian or quadratic differentials on an oriented surface of genus $g\geq 0$ with $m\geq 0$ punctures and $3g-3+m\geq 2$. We construct a subshift of finite type $(Ω,σ)$ and a Borel suspension of $(Ω,σ)$ which admits a finite-to-one semi-conjugacy into the Teichmueller flow $Φ^t$ on Q. This is used to show that the $Φ^t$-invariant Lebesgue measure on Q is the unique measure of maximal entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1112_6107 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Symbolic dynamics for the Teichmueller flow Hamenstädt, Ursula Dynamical Systems Geometric Topology 37A20, 30F60 Let Q be a component of a stratum of abelian or quadratic differentials on an oriented surface of genus $g\geq 0$ with $m\geq 0$ punctures and $3g-3+m\geq 2$. We construct a subshift of finite type $(Ω,σ)$ and a Borel suspension of $(Ω,σ)$ which admits a finite-to-one semi-conjugacy into the Teichmueller flow $Φ^t$ on Q. This is used to show that the $Φ^t$-invariant Lebesgue measure on Q is the unique measure of maximal entropy. |
| title | Symbolic dynamics for the Teichmueller flow |
| topic | Dynamical Systems Geometric Topology 37A20, 30F60 |
| url | https://arxiv.org/abs/1112.6107 |