Research Paper#Dynamical Systems, Time Delay Systems, Spectral Submanifolds, Inertial Manifolds🔬 ResearchAnalyzed: Jan 3, 2026 20:14
Existence of Spectral Submanifolds in Time Delay Systems
Published:Dec 26, 2025 15:32
•1 min read
•ArXiv
Analysis
This paper investigates the existence and properties of spectral submanifolds (SSMs) in time delay systems. SSMs are important for understanding the long-term behavior of these systems. The paper's contribution lies in proving the existence of SSMs for a broad class of spectral subspaces, generalizing criteria for inertial manifolds, and demonstrating the applicability of the results with examples. This is significant because it provides a theoretical foundation for analyzing and simplifying the dynamics of complex time delay systems.
Key Takeaways
- •Proves the existence of spectral submanifolds (SSMs) in time delay systems.
- •Establishes properties like smoothness, attractivity, and conditional uniqueness of SSMs.
- •Generalizes criteria for the existence of inertial manifolds.
- •Demonstrates the applicability of the results with examples.
Reference
“The paper shows existence, smoothness, attractivity and conditional uniqueness of SSMs associated to a large class of spectral subspaces in time delay systems.”