# About hyperbolic linear ordinary differential equations

I am seeking for a proof of the result that says:

$x'=Ax$ is hyperbolic iff there is no bounded orbit.

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 $x$ is a vector function and $A$ a matrix? – Simon S Jun 2 '12 at 20:09 It probably is. – checkmath Jun 2 '12 at 20:15 You should elaborate a bit more. Is $A$ a constant matrix? What does 'hyperbolic' mean? (This is why I downvoted. I will gladly reverse this if you edit your post satisfactorily). – Giuseppe Negro Jun 2 '12 at 22:36 the matrix A is a constant! – raymond Jun 3 '12 at 3:33