Question: Is there a way to obtain the fixed points of function?

Is there some command to find the fixed points of a function F(y)?. As my intuition suggests me.. it would not be possible to get the the values x such that x=F(x) for a general function, but.. which commands should I look at to get the values of x for a specific F (I would like to see that in the case of x is in R4.. that is x= (x1, x2, x3,x4)? Any answer will be really appreciated. J
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