Hamiltonian delay equations -- examples and a lower bound for the number of periodic solutions

Abstract

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 $(M,\omega )$ 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.

13 pages

References in corpus (2)

• The fine structure of Weber's hydrogen atom -- Bohr-Sommerfeld approach
• A compactness result for non-local unregularized gradient flow lines

Cited by in corpus (4)

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• State dependent Hamiltonian delay equations and Neumann one-forms
• An iterated graph construction and periodic orbits of Hamiltonian delay equations