\({C^{k}}\) Extension and Invariant Manifolds for the Compactification of Nonautonomous Systems with Autonomous Limits
Abstract
Abstract. We study the compactification of nonautonomous systems with autonomous limits and related dynamics. Although the [Formula: see text] extension of the compactification was well established, a great number of problems arising in bifurcation and stability analysis require the compactified systems with high-order smoothness. Inspired by this, we give a criterion for the [Formula: see text] ([Formula: see text]) extension of the compactification. After compactifying nonautonomous systems, the compactified systems may gain an additional center direction. We prove the existence and uniqueness of center or center-stable manifolds for normally hyperbolic compact invariant manifolds.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Stability and Controllability of Differential Equations
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- SIAM Journal on Applied Dynamical Systems
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 25
- Issue
- 2
- Pages
- 738–764
- Publication date
- 8 April 2026
- Language
- EN