2021/07/19 by Antoine Meddane, Meddane, Antoine · 1 citation
Computer Science · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Spectral Theory (math.SP) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2107.08875
openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.