Ruelle zeta function at zero for surfaces

Ruelle zeta function at zero for surfaces

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.

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Veröffentlicht in:Inventiones mathematicae 2017-10, Vol.210 (1), p.211-229
Hauptverfasser: Dyatlov, Semyon, Zworski, Maciej
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-017-0727-3