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SPECTRAL ANALYSIS OF MORSE–SMALE FLOWS I: CONSTRUCTION OF THE ANISOTROPIC SPACES

Part of: Partial differential equations on manifolds; differential operators Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  13 November 2018

Nguyen Viet Dang  and
Gabriel Rivière
Nguyen Viet Dang
Affiliation:
Institut Camille Jordan (U.M.R. CNRS 5208), Université Claude Bernard Lyon 1, Bâtiment Braconnier, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France (dang@math.univ-lyon1.fr)
Gabriel Rivière
Affiliation:
Laboratoire Paul Painlevé (U.M.R. CNRS 8524), U.F.R. de Mathématiques, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France (gabriel.riviere@math.univ-lille1.fr)
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Abstract

We prove the existence of a discrete correlation spectrum for Morse–Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with anisotropic Sobolev regularity on which the Lie derivative has a discrete spectrum.

Keywords

transfer operatorsPollicott–Ruelle resonancesMorse–Smale flowsMicrolocal analysis

MSC classification

Primary: 37D15: Morse-Smale systems
Secondary: 58J50: Spectral problems; spectral geometry; scattering theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 5 , September 2020 , pp. 1409 - 1465
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Copyright
© Cambridge University Press 2018

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