Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria





Citation of Original Publication


This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Attribution 4.0 International



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 ℝᵏ having any countable (finite) number of isolated equilibria for each k > 1.