Hamiltonian suspensions of symplectomorphisms: an alternative approach to design problems
The author deals with the problem that often arises in optics and charged particle transport systems. Note that in both cases the equations of motion are Hamiltonian, and in both cases one of them has control over what the system will actually be and one wants to specify that system. More precisely the author restricts himself to the following two mathematical problems: (a) Matching problem: For a given transformation from the input to the output to find some continuous Hamiltonian dynamics in between that produces the given transformation; (b) Design problem: For a given particular Hamiltonian, to produce many Hamiltonians that have the same time-one-map. The author finds solutions for both the matching and design problems that guarantee that the derived time-one symplectomorphism is exactly produced.
scientific article; zbMATH DE number 1374417