Hamiltonian suspensions of symplectomorphisms: an alternative approach to design problems

We solve the problem that often arises in optics and charged particle trans port design tasks of finding a time-dependent Hamiltonian system that produ ces a given symplectic map. In addition, we show how, given a particular Ha miltonian, to produce many Hamiltonians that have the same time-one map so that one has a large class of Hamiltonians from which to choose the 'best' design. We also show how to produce many symplectic maps that are given exp licitly rather than implicitly so that the design problem is more tractable . (C) 1999 Elsevier Science B.V. All rights reserved.