On symplectomorphisms and Hamiltonian flows (Q6601732)

In this paper, for a given symplectic diffeomorphism \(\psi\) which is close to the identity, the construction of a sequence of time one flows of autonomous Hamiltonian vector fields is proposed, such that the sequence converges to \(\psi\) exponentially fast. Such constructions are crucial in the Hamiltonian perturbation theory and this work gives a novel approach in a \(C^1\) environment for diffeomorphisms \(\psi\). The paper also contains a synopsis of the implicit Euler midpoint scheme given in the appendix.\N\NFor the entire collection see [Zbl 1515.53004].