Matthias Rumberger - Zentrum Mathematik, Technische Universität München, D-80290 München, Germany (email)
Abstract: A dynamical system equivariant with respect to a compact symmetry group induces a system on the orbit space. This (reduced) system inherits many important features of the given one, but the drifts along the group orbits disappear. Using invariant theory the orbit space along with the reduced system can be embedded into a real vector space. We consider the Lyapunov exponents of the reduced system, and prove formulas for these in terms of the Lyapunov exponents of the given system. These formulas enable us to make predictions about the latter using only the Lyapunov exponents of the reduced system.
Keywords: Lyapunov exponent, orbit space, Lie group, equivariant, dynamical
systems, orbital stability, Hilbert basis.
Received: February 2000; Revised: September 2000; Published: November 2000.
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