Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria
| dc.contributor.author | Arathoon, Philip | |
| dc.contributor.author | Kvalheim, Matthew D. | |
| dc.date.accessioned | 2023-10-25T14:07:33Z | |
| dc.date.available | 2023-10-25T14:07:33Z | |
| dc.date.issued | 2023-07-19 | |
| dc.description.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. | en_US |
| dc.description.uri | https://arxiv.org/abs/2306.15126 | en_US |
| dc.format.extent | 7 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m2xgxp-3viq | |
| dc.identifier.uri | https://doi.org/10.48550/arXiv.2306.15126 | |
| dc.identifier.uri | http://hdl.handle.net/11603/30368 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.rights | 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. | en_US |
| dc.rights | Attribution 4.0 International | * |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | * |
| dc.title | Koopman Embedding and Super-Linearization Counterexamples with Isolated Equilibria | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-2662-6760 | en_US |