Lyapunov exponents on the orbit space

A dynamical system equivariant with respect to a compact symmetry group ind uces a system on the orbit space. This (reduced) system inherits many impor tant features of the given one, but the drifts along the group orbits disap pear. Using invariant theory the orbit space along with the reduced system can be embedded into a real vector space. We consider the Lyapunov exponent s of the reduced system, and prove formulas for these in terms of the Lyapu nov exponents of the given system. These formulas enable us to make predict ions about the latter using only the Lyapunov exponents of the reduced syst em.