Definition For Flows
Given a real dynamical system (T, X, φ) with flow, a point x and an orbit γ through x, we call a point y an ω-limit point of γ if there exists a sequence in R so that
- .
Analogously we call y an α-limit point if there exists a sequence in R so that
- .
The set of all ω-limit points (α-limit points) for a given orbit γ is called ω-limit set (α-limit set) for γ and denoted limω γ (limα γ).
If the ω-limit set (α-limit set) is disjunct from the orbit γ, that is limω γ ∩ γ = ∅ (limα γ ∩ γ = ∅), we call limω γ (limα γ) a ω-limit cycle (α-limit cycle).
Alternatively the limit sets can be defined as
and
Read more about this topic: Limit Set
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