REVIEW 2 cited by
Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
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 admitting a smooth embedding as an invariant submanifold of a linear dynamical system. This claim is sometimes made only for the class of super-linearizations, which additionally require that the embedding "contain the state''. We show that both versions of this claim are false by constructing (super-)linearizable smooth dynamical systems on $\mathbb{R}^k$ having any countable (finite) number of isolated equilibria for each $k>1$.
Forward citations
Cited by 2 Pith papers
-
Global linearization of asymptotically stable systems without hyperbolicity
Asymptotically stable nonlinear systems admit global linearizing coordinates, smoothly off the equilibrium in every dimension except 5, where existence is equivalent to the smooth 4D Poincaré conjecture.
-
Data-Driven Model Identification Using Time Delayed Nonlinear Maps for Systems with Multiple Attractors
A hybrid of extended and higher-order dynamic mode decomposition, trained with trajectories from every basin of attraction, can identify nonlinear systems with multiple attractors and approximate boundaries between them.
Discussion (0). Continue with ORCID to comment.