Cuplength estimates for periodic solutions of Hamiltonian particle-field systems
Cuplength estimates for periodic solutions of Hamiltonian particle-field systems
Abstract 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 $${\mathbb {T}}^d={\mathbb {R}}^d/(2\pi {\mathbb {Z}})^d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup><mml:mo>/</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:mrow></mml:math> and the coordinates of the particles are …