Definition:Invariant Set/Negatively Invariant

Definition

Let $S$ be a set.

Let $f: S \to S$ be a self-map on $S$.

Let $T \subseteq S$ be a subset of $S$ such that:

$f^{-1} \sqbrk T \subseteq T$

Then $T$ is a negatively invariant set of $f$.

Also see

• Definition:Invariant Set
• Definition:Positively Invariant Set

Sources

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