THE GENERICITY OF ARNOLD DIFFUSION IN NEARLY INTEGRABLE HAMILTONIAN SYSTEMS

In this paper, we prove that the net of transition chain is delta-dense for nearly integrable positive definite Hamiltonian systems with 3 degrees of freedom in the cusp-residual generic sense in C-r-topology, r >= 6. The main ingredients of the proof existed in [CZ, C17a, C17b]. As an immediate consequence, Arnold diffusion exists among this class of Hamiltonian systems. The question of [C17c] is answered in Section 9 of the paper.