Definition:Positively Invariant Set of a Map

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Definition

Let $f:X\to X$ be a map on an underlying space $X$.

Then a subset $Y\subset X$ is a positively invariant set of $f$ if $f(Y) \subset Y$.

Also see

• Definition:Invariant Set of a Map
• Definition:Negatively Invariant Set of a Map

Sources

• 1999: Clark Robinson: Dynamical Systems: Stability, Symbolic Dynamics, and Chaos ... (previous) ... (next): Chapter $\text {II}$ $\S 2.3$.