# Cuplength estimates for periodic solutions of Hamiltonian particle-field systems

@inproceedings{Fabert2021CuplengthEF, title={Cuplength estimates for periodic solutions of Hamiltonian particle-field systems}, author={O. Fabert and N. Lamoree}, year={2021} }

We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus T = R /(2π Z) and the coordinates of the particles are constrained to a submanifold Q ⊂ T, we prove that the number of T -periodic solutions of the coupled Hamiltonian particle-field system is bounded from below by the Z2-cuplength of the space ΛQ of… Expand

#### 2 Citations

Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves.

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We prove the existence of a forced time-periodic solution to general nonlinear Hamiltonian PDEs by using pseudoholomorphic curves as in symplectic homology theory. When the nonlinearity is… Expand

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After our compactness result in [FL19], we continue our program for defining a Floer homology theory for Hamiltonian partial differential equations with regularizing nonlinearities. Despite the… Expand

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