On groups acting in phase space

The problem of the motion of a material point in a central field of general type is considered. It is shown that in the infinite-dimensional group of canonical transformations which leave the Hamiltonian function invariant there are no finite-dimensional subgroups which are significantly larger than the three-dimensional group of rotations (exact formulations in Sec. 3 and Sec. 5).Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 55–61, January, 1969.I am indebted to A. A. Kirillov for helpful discussions.