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morse–smale flows

Journal of the Institute of Mathematics of Jussieu (1)

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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
Nguyen Viet Dang, Gabriel Rivière
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 5 / September 2020

Published online by Cambridge University Press:

13 November 2018, pp. 1409-1465

Print publication:

September 2020
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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.