Lyapunov exponents on the orbit space

Matthias Rumberger

doi:10.3934/dcds.2001.7.91

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2001, Volume 7, Issue 1: 91-113. Doi: 10.3934/dcds.2001.7.91

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Lyapunov exponents on the orbit space

Matthias Rumberger^1,

1.
Zentrum Mathematik, Technische Universität München, D-80290 München

Received: January 31, 2000

Revised: August 31, 2000

Published: December 2000

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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.

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Mathematics Subject Classification: 34D08, 57S15, 58F11.

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