Topology of Pollicott-Ruelle resonant states

@article{Dang2017TopologyOP,
  title={Topology of Pollicott-Ruelle resonant states},
  author={Nguyen Viet Dang and Gabriel Rivi{\`e}re},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associated with Anosov and Morse--Smale flows. As a consequence, weobtain generalized Morse inequalities for such flows. In the case of Morse--Smale flows,we relate the resonances lying on the imaginary axis with the twisted Fuller measuresused by Fried in his work on Reidemeister torsion. In particular, when V is a… Expand
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