Linearization of Cohomology-free Vector Fields

Livio Flaminio (1) , Miguel Paternain

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group.

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]

Livio Flaminio, Miguel Paternain. Linearization of Cohomology-free Vector Fields. Discrete and Continuous Dynamical Systems - Series A, 2011, pp.Pages: 1031 - 1039, Volume: 29 Issue: 3. ⟨10.3934/dcds.2011.29.1031⟩. ⟨hal-00805405⟩