Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria
Links to Files
Collections
Author/Creator
Author/Creator ORCID
Date
Type of Work
Department
Program
Citation of Original Publication
Rights
Attribution 4.0 International
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.
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.
Subjects
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 ℝᵏ having any countable (finite) number of isolated equilibria for each k > 1.