Abstract
It is shown that a nonstationary evolution equation solution admits two universal representations. The first is a canonical factorization into an infinite product of exponentials. This representation involves a nonstandard “integral type” Lie algebra from which an extended Hall set can be extracted. This result can be thought of as the formal continuous analogue of a Lazard factorization of the free monoid.
It is also shown that a second canonical representation into a single exponential is possible, thus making an earlier work of Magnus [6], continued by Michel [14], more precise. In the sequel, reverse time together with duality problems are discussed. Finally, the evolution operator for a general Lie derivative is shown to lead to tractable combinatorial problems.
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Huillet, T., Monin, A. & Salut, G. Lie algebraic representation results for nonstationary evolution operators. Math. Systems Theory 19, 205–226 (1986). https://doi.org/10.1007/BF01704914
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DOI: https://doi.org/10.1007/BF01704914