Stability analysis of dynamical regimes in nonlinear systems with discrete symmetries.
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.
Chechin
G M
GM
Department of Physics, Rostov State University, Rostov-on-Don 344090, Russia. chechin@phys.rsu.ru
Zhukov
K G
KG