On the Density of Periodic Measures for Star Vector Fields
Abstract
In this paper, we prove that every ergodic hyperbolic invariant measure of a $C^1$ star vector field can be approximated by periodic measures in weak$^*$ topology. This extends a classical result of Katok \cite{Ka} for $C^{1+α}(α>0)$ diffeomorphisms to $C^1$ star vector field of any dimension.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Advanced Topology and Set Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 February 2026
- Document type
- Preprint