denoted limω γ (limα γ). If the ω-limit set (α-limit set) is disjoint 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 Examples For any periodic orbit γ of a dynamical system, limω γ = limα γ = γ For any fixed point of a dynamical system, limω = limα = Properties limω γ and limα γ are closed if X is compact then limω γ and limα γ are nonempty, compact and connected limω γ and limα γ are φ-invariant, that is φ( × limω γ) = limω γ and φ( × limα γ) = limα γ See also Julia set Stable set Limit cycle Periodic point Non-wandering set Kleinian group References Further reading