Đề tài " A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4 "

We construct a proper C 2 -smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2 -smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. 1. Introduction The “Hamiltonian Seifert conjecture” is the question whether or not there exists a proper function on R2n whose Hamiltonian flow has no periodic orbits on at least one regular level set.