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

Published online by Cambridge University Press:  13 November 2018

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 ([email protected])
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 ([email protected])

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.

Type
Research Article
Copyright
© Cambridge University Press 2018

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