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This method is likely worse than nearly any other in existence, since it does not converge to the correct value in any particular fixed-precision system, since all orbits are ultimately periodic, and the Lyapunov exponent of a periodic orbit is the logarithm of an algebraic number, which can't be unless is a special algebraic number, namely the P-th root (for some integer P) of a quadratic irrational.

Yet this qualifies as a genuine method, since in principle you could implement higher and higher precision floating-point systems and achieve the desired accuracy by longer and longer runs with this high-precision arithmetic. Of course this is impractical, perhaps even ridiculous. There is also the problem of choosing ``good'' initial points---if we are lucky, the first initial point we choose for whatever floating-point system we have will do the trick---but there is no guarantee, and indeed the Lyapunov exponent may converge to something totally different (or worse, something only slightly different). [an error occurred while processing this directive]

This method is clearly related to the Monte Carlo methods [23], with the roundoff error associated with the floating-point arithmetic playing the part of the random number generator required.

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