A Comparison Theorem for Hamiltonian Vector Fields

Alan Weinstein, Jerrold Marsden
1970 Proceedings of the American Mathematical Society  
The question of completeness of Hamiltonian systems is investigated for a class of potentials not necessarily bounded below. The result generalizes previous work of W. Gordon and D. Ebin. This paper extends the completeness theorem of Ebin [l] to include certain potential functions V not necessarily bounded below. The condition on V is essentially the same as a condition for a corresponding quantum mechanical theorem. See [3] and Remark 3 below. We shall prove a comparison theorem which reduces
more » ... eorem which reduces the general case to the one-dimensional case, so we begin with the latter. Received by the editors March 15, 1970. A MS 1969 subject classifications. Primary 3465; Secondary 3442. Key words and phrases. Complete vector field, infinite-dimensional manifold, Hamiltonian vector field, dissipative system.
doi:10.2307/2037123 fatcat:syvwaxptq5fi5k7wxb4boi3lpu