Ginzburg is best known for his work on the Conley conjecture,[1] which asserts the existence of infinitely many periodic points for Hamiltonian diffeomorphisms in many cases, and for his counterexample (joint with Başak Gürel) to the Hamiltonian Seifert conjecture[2] which constructs a Hamiltonian with an energy level with no periodic trajectories.
Ginzburg was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to Hamiltonian dynamical systems and symplectic topology and in particular studies into the existence and non-existence of periodic orbits".[5]