Hamiltonian delay equations: examples and a lower bound for the number of periodic solutions
We describe a variational approach to a notion of Hamiltonian delay equations. Our delay Hamiltonians are of product form. We consider several examples. For closed symplectically aspherical symplectic manifolds (M,ω) we prove that for generic delay Hamiltonians the number of 1-periodic solutions of...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
31 July 2020
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| In: |
Advances in mathematics
Year: 2020, Jahrgang: 373 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2020.107319 |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1016/j.aim.2020.107319 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0001870820303455 
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| Verfasserangaben: | Peter Albers, Urs Frauenfelder, Felix Schlenk |
| Zusammenfassung: | We describe a variational approach to a notion of Hamiltonian delay equations. Our delay Hamiltonians are of product form. We consider several examples. For closed symplectically aspherical symplectic manifolds (M,ω) we prove that for generic delay Hamiltonians the number of 1-periodic solutions of the Hamiltonian delay equation is at least the sum of the Betti numbers of M, extending the proof of the Arnold conjecture to the case with delay. |
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| Beschreibung: | Gesehen am 17.02.2022 |
| Beschreibung: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2020.107319 |