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I was reading a paper about the reducibility of linear functional differential equations with quasi periodic coefficients. The paper talks about the asymptotic reducibility of systems. I don't the definition of asymptotic reducibility of system. Could someone tell me the definition of that and give me a good reference to get more about it ? Thank you.

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Well it depends on the paper, usually in that kind of problems reducibility means that you may find a change of coordinate that put your system in an other one whose coefficients are time independent. Asymptotic I can image that they are not able to find a change of coordinates that tranform your system in an other one whose coefficients are time independent, but maybe they are able to find $n$ transformation such that the first $n$ term of are time independent. But you always have a time dependent remainder. Maybe if you link the paper I try to understand.

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