2025/12/08 by Erchenko, Alena, Vinhage, Kurt, Yang, Yun
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2512.08051
openalex publication_date 2025/12/08 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
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.