Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Dynamical Systems
2025-12-10 v1 Symplectic Geometry
Abstract
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact flow, we show the existence of a normal form for the contact form what results in an improved normal form for its Reeb vector field. Additionally, we present a few rigidity results associated to periodic data for Anosov contact flows derived from the underlying normal form theory. Finally, we establish a new local rigidity result for contact flows on manifolds of dimension 3 in a neighborhood of a hyperbolic periodic point by finding a new link between the roof function and the return map to a section.
Cite
@article{arxiv.2512.08051,
title = {Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3},
author = {Alena Erchenko and Kurt Vinhage and Yun Yang},
journal= {arXiv preprint arXiv:2512.08051},
year = {2025}
}