What is the relationship between periodic points and invariant points?
Is every periodic points an invariant point?
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Could you say more about the context? – Mundron Schmidt Jun 02 '17 at 10:54
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A periodic point is a point $p$ such that $f^m(p)=p$ for some (smallest) integer $m \geq 1$. If $m=1$, it is an invariant point (more commonly called a fixed point).
So every fixed point is a periodic point, but the converse is not true.
Albert
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sure, take $f(z)=-z$: then $p=1$ is a periodic point of period 2 since $f(1)=-1 \neq 1$ and $f(f(1))=-(-1))=1$. – Albert Jun 02 '17 at 11:46