Lyapunov exponents on the orbit space
Matthias Rumberger
Discrete & Continuous Dynamical Systems - A 2001, 7(1): 91-113 doi: 10.3934/dcds.2001.7.91
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: Lie group orbit space equivariant Hilbert basis. orbital stability Lyapunov exponent dynamical systems

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