Lyapunov Exponents of Symmetric Attractors

P. Aston and I. Melbourne. Lyapunov exponents of symmetric attractors. Nonlinearity 19 (2006) 2455-2466

Philip Aston and Ian Melbourne


Abstract

The Lyapunov exponents of symmetric attractors can be forced to be multiple by ``instantaneous symmetries'' which fix the attractor pointwise. In this paper, we show that ``symmetries on average'' which fix the attractor as a set may lead to further multiplicities. This work is motivated by, and provides an explanation for, numerical computations by Aston & Laing of Lyapunov exponents for the complex Ginzburg-Landau equation.


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