Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits
| dc.contributor.author | Kvalheim, Matthew D. | |
| dc.contributor.author | Hong, David | |
| dc.contributor.author | Revzen, Shai | |
| dc.date.accessioned | 2023-10-25T13:36:54Z | |
| dc.date.available | 2023-10-25T13:36:54Z | |
| dc.date.issued | 2021-07-16 | |
| dc.description.abstract | Our recent work established existence and uniqueness results for Cᵏ (actually Cᵏᵃ ₗₒ꜀ ) linearizing semiconjugacies for C flows defined on the entire basin of an attracting hyperbolic fixed point or periodic orbit (Kvalheim and Revzen, 2019). Applications include (i) improvements, such as uniqueness statements, for the Sternberg linearization and Floquet normal form theorems, and (ii) results concerning the existence, uniqueness, classification, and convergence of various quantities appearing in the “applied Koopmanism” literature, such as principal eigenfunctions, isostables, and Laplace averages. In this work we consider the broadness of applicability of these results with an emphasis on the Koopmanism applications. In particular we show that, for the flows of “typical” c∞ vector fields having an attracting hyperbolic fixed point or periodic orbit with a fixed basin of attraction, the c∞ Koopman eigenfunctions can be completely classified, generalizing a result known for analytic eigenfunctions of analytic systems. | en |
| dc.description.sponsorship | Kvalheim and Revzen were supported by ARO award W911NF14-1-0573 to Revzen and by the ARO under the Multidisciplinary University Research Initiatives (MURI) Program, award W911NF17-1-0306 to Revzen. Kvalheim was also supported by the ARO under the SLICE MURI Program, award W911NF-18-1-0327. Hong was supported in part by the Dean’s Fund for Postdoctoral Research of the Wharton School. | |
| dc.description.uri | https://www.sciencedirect.com/science/article/pii/S2405896321006443 | en |
| dc.format.extent | 6 pages | en |
| dc.genre | conference papers and proceedings | en |
| dc.identifier | doi:10.13016/m2ftz4-mccm | |
| dc.identifier.citation | Kvalheim, Matthew D., David Hong, and Shai Revzen. “Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits.” IFAC-PapersOnLine, 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020, 54, no. 9 (January 1, 2021): 267–72. https://doi.org/10.1016/j.ifacol.2021.06.150. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.ifacol.2021.06.150 | |
| dc.identifier.uri | http://hdl.handle.net/11603/30366 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.rights | Attribution-NonCommercial-NoDerivs 4.0 International | * |
| 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 |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.title | Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits | en |
| dc.type | Text | en |
| dcterms.creator | https://orcid.org/0000-0002-2662-6760 | en |