The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral. (English. Russian original) Zbl 0598.58026
Russ. Math. Surv. 39, No. 4, 133-134 (1984); translation from Usp. Mat. Nauk 39, No. 4(238), 173-174 (1984).
We prove in this note that the Bogoyavlenskij-Novikov principle is valid for all Hamiltonian formalisms. In addition, we prove that the Hamiltonian condition on the original non-stationary problem is not at all essential. A more general principle holds: every translation- invariant evolutionary flow is Hamiltonian on the set of stationary points of its local integral.
MSC:
37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
37C10 | Dynamics induced by flows and semiflows |