Towards the theory of Hamiltonian systems with an external action
The author considers the Hamiltonian system with an external action and \(N\) degrees of freedom. First, he ensures the existence and uniqueness of a solution at least on the positive semiaxis of time. Then he establishes the final boundedness of the total mechanical energy on all solutions. The energy boundedness is very important in applications, because it can serve as a measure of stability of physical systems under structural perturbations. Finally, the author describes asymptotic properties of solutions in the past. If one continues any solution in the past, then the value of the Hamiltonian either increases unboundedly or is uniformly bounded.
scientific article; zbMATH DE number 1050479