Can someone suggest a reference on the mathematical results (NOT numerical) on the Lyapunov exponents of Lorenz-63 and Lorenz-96 systems (or any other non-trivial system)? In particular, is it always the case that at least one of the Lyapunov exponents (eg. for a flow that has bounded range when time --> infty) must be 0? Is there any method to find the Lyapunov exponents beyond numerical calculation?
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$\begingroup$ The positive Lyapunov exponent of Lorenz-63 is at least $2^{1/29}$, see section 4 of dx.doi.org/10.1016/S0764-4442(99)80439-X -- PDF at www2.math.uu.se/~warwick/main/papers/comptes.pdf $\endgroup$– Steve HuntsmanCommented Apr 26, 2016 at 16:40
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$\begingroup$ @SteveHuntsman Thanks for the suggestion. The paper is of 17 years ago though. Is this the newest rigorous result about the Lyapunov exponent of L63 system? $\endgroup$– Yicun ZhenCommented Apr 26, 2016 at 16:49
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