Status: Bibliographieeintrag
Standort: ---
Exemplare:
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| Online-Ressource |
Verfasst von: | Albers, Peter [VerfasserIn]  |
| Seifert, Irene [VerfasserIn]  |
Titel: | Periodic delay orbits and the polyfold implicit function theorem |
Verf.angabe: | Peter Albers, Irene Seifert |
E-Jahr: | 2022 |
Jahr: | 7 July 2022 |
Umfang: | 30 S. |
Fussnoten: | Gesehen am 11.08.2022 |
Titel Quelle: | Enthalten in: Commentarii mathematici Helvetici |
Ort Quelle: | Zürich : EMS Publ. House, 1929 |
Jahr Quelle: | 2022 |
Band/Heft Quelle: | 97(2022), 2, Seite 383-412 |
ISSN Quelle: | 1420-8946 |
Abstract: | We consider differential delay equations of the form partial derivative(t)x(t) = X-t(x(t-tau)) in R-n, where (X-t)(t is an element of S)1 is a time-dependent family of smooth vector fields on R-n and tau is a delay parameter. If there is a (suitably non-degenerate) periodic solution x(0) of this equation for tau = 0, that is without delay, there are good reasons to expect existence of a family of periodic solutions for all sufficiently small delays, smoothly parametrized by tau. However, it seems difficult to prove this using the classical implicit function theorem, since the equation above, considered as an operator, is not smooth in the delay parameter. In this paper, we show how to use the M-polyfold implicit function theorem by Hofer-Wysocki-Zehnder (2009, 2021) to overcome this problem in a natural setup. |
DOI: | doi:10.4171/CMH/533 |
URL: | Bitte beachten Sie: Dies ist ein Bibliographieeintrag. Ein Volltextzugriff für Mitglieder der Universität besteht hier nur, falls für die entsprechende Zeitschrift/den entsprechenden Sammelband ein Abonnement besteht oder es sich um einen OpenAccess-Titel handelt.
Volltext ; Verlag: https://doi.org/10.4171/CMH/533 |
| Volltext: https://www.webofscience.com/api/gateway?GWVersion=2&SrcAuth=DynamicDOIArticle&SrcApp=WOS&KeyAID=10.4171%2FCMH%2F533&Des ... |
| DOI: https://doi.org/10.4171/CMH/533 |
Datenträger: | Online-Ressource |
Sprache: | eng |
Sach-SW: | Delay differential equations |
| differential-equations |
| implicit function theorem |
| periodic orbits |
| polyfold theory |
K10plus-PPN: | 1814178260 |
Verknüpfungen: | → Zeitschrift |
Periodic delay orbits and the polyfold implicit function theorem / Albers, Peter [VerfasserIn]; 7 July 2022 (Online-Ressource)
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