A Morse complex for Axiom A flows
Dynamical Systems
2021-07-20 v1 Geometric Topology
Spectral Theory
Abstract
On a smooth compact Riemannian manifold without boundary, we construct a finite dimensional cohomological complex of currents that are invariant by an Axiom A flow verifying Smale's transversality assumptions. The cohomology of that complex is isomorphic to the De Rham cohomology via certain spectral projectors. This construction is achieved by defining anisotropic Sobolev spaces adapted to the global dynamics of Axiom A flows. In the particular case of Morse-Smale gradient flows, this complex coincides with the classical Morse complex.
Keywords
Cite
@article{arxiv.2107.08875,
title = {A Morse complex for Axiom A flows},
author = {Antoine Meddane},
journal= {arXiv preprint arXiv:2107.08875},
year = {2021}
}