Bowen's construction for the Teichmueller flow

Hamenstaedt, Ursula

doi:10.48550/arxiv.1007.2289

Cited by 2 publications

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“…In this section we summarize some constructions from [T79,PH92,H10c] which will be used throughout the paper. Furthermore, we introduce a class of train tracks which will be important in the later sections, and we discuss some of their properties.…”

Section: Train Tracks and Geodesic Laminationsmentioning

confidence: 99%

Symbolic dynamics for the Teichmueller flow

Hamenstaedt

2011

Preprint

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Let S be an oriented surface of genus g ≥ 0 with m ≥ 0 punctures and 3g −3+m ≥ 2. The Teichmüller flow Φ t acts on the moduli space Q(S) (or H(S)) of area one holomorphic quadratic (or abelian) differentials preserving a collection of so-called strata. For each component Q of a stratum, we construct a subshift of finite type (Ω, σ) and Borel suspension (X, Θ t ) which admits a finite-to-one semi-conjugacy Ξ into the Teichmüller flow on Q. This is used to show that the Φ t -invariant Lebesgue measure λ on Q is the unique measure of maximal entropy. If h is the entropy of λ then for every ǫ > 0 there is a compact set K ⊂ Q such that the entropy of any Φ t -invariant probability measure µ with µ(Q − K) = 1 does not exceed h − 1 + ǫ. Moreover, the growth rate of periodic orbits in Q − K does not exceed h − 1 + ǫ. This implies that the number of periodic orbits for Φ t in Q of period at most R is asymptotic to e hR /hR. Finally we give a unified and simplified proof of exponential mixing for the Lebesgue measure on strata.

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Section: Train Tracks and Geodesic Laminationsmentioning

confidence: 99%

Symbolic dynamics for the Teichmueller flow

Hamenstaedt

2011

Preprint

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“…Suspension flows over countable Markov shifts serve as useful models for a wide variety of flows on non-compact spaces, such as the geodesic flow on the modular surface and the Teichmüller flow, and so having an effective notion of topological pressure for such suspension flows will allow the techniques of thermodynamic formalism to be applied to these related systems. Indeed, there is already a large volume of recent work applying the definitions of [2,12] to the study of systems modelled by suspension flows over countable Markov shifts, see, for example, [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic formalism for suspension flows over countable Markov shifts

Kempton¹

2011

Nonlinearity

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We introduce a new notion of topological pressure for suspension flows over countable Markov shifts. We show that our definition, which is a natural analogue of Gurevich pressure for a Markov shift, is equivalent to previous notions of topological pressure which were defined on a restricted class of flows. We also widen the domain of definition of these previous notions, making them suitable for application to some important examples.

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Bowen's construction for the Teichmueller flow

Cited by 2 publications

References 0 publications

Symbolic dynamics for the Teichmueller flow

Symbolic dynamics for the Teichmueller flow

Thermodynamic formalism for suspension flows over countable Markov shifts

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