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  "body": "\n## Summary\n\nThe Floquet multipliers of a linear system with periodic coefficients are the eigenvalues of its monodromy matrix, the map that advances solutions by one period.\nThey play the role that the values $e^{\\lambda T}$ play for a system with constant coefficients.\nThey decide whether solutions grow, decay or stay bounded, and they measure the stability of a [[periodic orbit|0AA97XA70K]] of a nonlinear system.\nThey are the central notion of [[Floquet theory|BJVZXPB297]].\nSee the [[definition|GVSY2FZ8YW]].\n\n## Explanations\n\n### L1 human\n\nWatch a solution of a periodic linear system only at the times $0, T, 2T, \\ldots$, once per period.\nFrom one snapshot to the next, the state is multiplied by a fixed matrix $M$.\nThe eigenvalues of $M$ are the Floquet multipliers.\nIf all have absolute value less than $1$, every solution shrinks to $0$; if one has absolute value greater than $1$, some solution grows without bound.\nFor the scalar equation $x' = (1 + \\cos t)\\, x$, one period multiplies $x$ by $e^{2\\pi}$, so the multiplier is $e^{2\\pi}$.\n",
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