Definition:Omega-Limit Point

Definition

Let $\struct {X, f}$ be a topological dynamical system.

Let $x \in X$.

Then $y \in X$ is a $\omega$-limit point of $x$ if and only if $\exists \sequence {n_k} \subseteq \N$ such that:

$\ds \lim_{k \mathop \to \infty} n_k = +\infty$

and:

$\ds y = \lim_{k \mathop \to \infty} \map {f^{n_k} } x$

where $f^n$ denotes the $n$th power of $f$.

Also see

• Definition:Omega-Accumulation Point

Sources

• 2002: Michael Brin and Garrett Stuck: Introduction to Dynamical Systems $2.1$: Limit Sets and Recurrence