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math.DS2023★ 2 cited
Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria
Philip Arathoon, Matthew D. Kvalheim
A frequently repeated claim in the "applied Koopman operator theory'' literature is that a dynamical system with multiple isolated equilibria cannot be linearized in the sense of a…
math.DS2016
Reverse-engineering invariant manifolds with asymptotic phase
Matthew Kvalheim, Shai Revzen
We present a recipe for rendering a submanifold normally hyperbolic and invariant within a stability basin. The construction includes the ability to choose the asymptotic phase map…