Forward-invariant set
= Forward-invariant set
{title2=$F(S)\subseteq S$}
= Forward invariant
{synonym}
A subset of a <dynamical system> is <forward-invariant set>[forward invariant] if every forward iterate, or every forward-time trajectory beginning in the set, stays in it. For a <discrete dynamical system>[map] $F$, this means $F(S)\subseteq S$. It does not require backward invariance or equality $F(S)=S$. Such sets give useful positivity and boundedness guarantees.