KAM theorems for the product of two involutions of different types.
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.
Quispel
G. R. W.
GR
Department of Mathematics, La Trobe University, Bundoora, Melbourne 3083, AustraliaInstitute of Energy Problems of Chemical Physics, 117829, Lenin Prospect 38, Building 2, Moscow, Russia.
Sevryuk
M. B.
MB