Definition:Omega-Limit Point
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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
Sources
- 2002: Michael Brin and Garrett Stuck: Introduction to Dynamical Systems $2.1$: Limit Sets and Recurrence