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Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n","lang":"eng"}],"user_id":"49178","language":[{"iso":"eng"}],"date_updated":"2022-05-19T10:13:48Z","doi":"10.1007/s00220-020-03793-2","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","title":"Pollicott-Ruelle Resonant States and Betti Numbers"}]