Under what conditions on the matrix A can the linear differential equation dx/dt = Ax where x = (x1,x2....,xn)^T have periodic solutions?

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- Aug 23rd 2012, 07:32 AMNFS1linear differential equation - periodic solutions
Under what conditions on the matrix A can the linear differential equation dx/dt = Ax where x = (x1,x2....,xn)^T have periodic solutions?

- Aug 23rd 2012, 07:37 AMHallsofIvyRe: linear differential equation - periodic solutions
If and only if the matrix A has pure imaginary eigenvalues.

- Aug 26th 2012, 04:46 AMNFS1Re: linear differential equation - periodic solutions
- Aug 26th 2012, 04:55 AMProve ItRe: linear differential equation - periodic solutions
- Aug 27th 2012, 04:15 PMNFS1Re: linear differential equation - periodic solutions