Construction of exact invariants for time-dependent classical dynamical systems
This paper reviews various methods for the construction of exact invariants for classical Hamiltonian dynamical systems with an explicit time dependence. One- and two-dimensional systems are discussed in detail, providing a classification of these systems from the point of view of exact invariants. Special sections are devoted to Ermakov systems and to the integrability of non-central two-dimensional time-dependent systems. Additionally, the author mentions a number of physical applications of the above invariants. It appears that the reviewed literature is essentially limited to physics and mathematical physics, with little attention to journals devoted to differential equations and/or analysis; this is entirely justified considering the journal in which this paper appears and the kind of applications considered. The reviewer points out that for time-independent systems similar problems have been discussed by \textit{J. Hietarinta} [Phys. Rep. 147, 87-154 (1987)] the applications of the Painlevé conjecture to such systems have been reviewed by \textit{M. Lakshmanan} and \textit{R. Sahadevan} [Phys. Rep. 224 (1993)].
scientific article; zbMATH DE number 1337696