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In page Dynamical system:

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The map Φ embodies the time evolution of the dynamical system. Thus, for discrete dynamical systems the iterates Φ n = Φ ∘ Φ ∘ ⋯ ∘ Φ {\displaystyle \Phi ^{n}=\Phi \circ \Phi \circ \dots \circ \Phi } for every integer n are studied[citation needed]. For continuous dynamical systems, the map Φ is understood to be a finite time evolution map and the construction is more complicated.[citation needed]