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What are Lyapunov exponents?

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What are Lyapunov exponents?

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(Thanks to Ronnie Mainieri & Fred Klingener for contributing to this answer) The hardest thing to get right about Lyapunov exponents is the spelling of Lyapunov, which you will variously find as Liapunov, Lyapunof and even Liapunoff. Of course Lyapunov is really spelled in the Cyrillic alphabet: (Lambda)(backwards r)(pi)(Y)(H)(0)(B). Now that there is an ANSI standard of transliteration for Cyrillic, we expect all references to converge on the version Lyapunov. Lyapunov was born in Russia in 6 June 1857. He was greatly influenced by Chebyshev and was a student with Markov. He was also a passionate man: Lyapunov shot himself the day his wife died. He died 3 Nov. 1918, three days later. According to the request on a note he left, Lyapunov was buried with his wife. [biographical data from a biography by A. T. Grigorian]. Lyapunov left us with more than just a simple note. He left a collection of papers on the equilibrium shape of rotating liquids, on probability, and on the stability of l

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