Trajectories of vector fields asymptotic to formal invariant curves
Abstract
Abstract We prove that a formal curve Γ $\Gamma $ normal upper Gamma that is invariant by a C ∞ $C^{\infty }$ upper C Superscript infinity vector field ξ $\xi $ xi of R m $\mathbb R^{m}$ double struck upper R Superscript m has a geometrical realization, as soon as the Taylor expansion of ξ $\xi $ xi is not identically zero along Γ $\Gamma $ normal upper Gamma . This means that there is a trajectory γ ⊂ R m $\gamma \subset \mathbb R^{m}$ gamma subset of double struck upper R Superscript m of ξ $\xi $ xi which is asymptotic to
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Mathematics and Applications
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Publisher
- Cambridge University Press (CUP)
- Volume
- 46
- Issue
- 9
- Pages
- 2245–2276
- Publication date
- 1 April 2026
- Language
- EN