Existence of multiple periodic orbits of Hamiltonian systems on positive-type hypersurfaces in [formula omitted

Abstract

This paper deals with the fixed energy problem of Hamiltonian systems in R2n. The main result is an existence theorem of multiple periodic orbits for Hamiltonian vector fields on a class of contact type but not necessarily star-shaped hypersurfaces. This is the first multiplicity result for hypersurfaces that are more general than star-shaped ones. The main result is achieved by using critical point theory for a special Hamiltonian function, and central gravity of the proof relies on a delicate construction of such Hamiltonian function.