Ruelle zeta function at zero for surfaces

• 成果类型: Article
• 署名作者: Dyatlov, Semyon; Zworski, Maciej
• 署名单位: Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0727-3
• 发表日期: 2017
• 页码: 211-229
• 关键词: contact anosov-flows; fredholm determinants; hyperbolic manifolds; DYNAMICAL-SYSTEMS; analytic-torsion; sobolev spaces; MAPS; diffeomorphisms; resonances; spectrum

摘要

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.