title: KAM theorems for the product of two involutions of different types.
abstract: The properties of quasiperiodic motions in Hamiltonian, volume preserving, and reversible systems are summarized. KAM theorems concerning lower-dimensional invariant tori are announced for G-reversible mappings A such that the fixed point manifolds Fix(G) and Fix(AG) of the reversing involutions G and AG are of different dimensions. The case where the manifold Fix(G) itself consists of several connected components of different dimensions is also briefly discussed.
authors.affiliation: Department of Mathematics, La Trobe University, Bundoora, Melbourne 3083, AustraliaInstitute of Energy Problems of Chemical Physics, 117829, Lenin Prospect 38, Building 2, Moscow, Russia.
authors.forename: G. R. W.
authors.initials: GR
authors.lastname: Quispel
authors.forename: M. B.
authors.initials: MB
authors.lastname: Sevryuk