title: Stability analysis of dynamical regimes in nonlinear systems with discrete symmetries.
abstract: We present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems with different kinds of discrete symmetry. This theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system. As an example of such a simplification, we discuss the stability of bushes of modes (invariant manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the maximal dimension of the above-mentioned subsystems.
authors.affiliation: Department of Physics, Rostov State University, Rostov-on-Don 344090, Russia. chechin@phys.rsu.ru
authors.forename: G M
authors.initials: GM
authors.lastname: Chechin
authors.forename: K G
authors.initials: KG
authors.lastname: Zhukov