Page "Dynamical system" Paragraph 11
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A dynamical system is a manifold M called the phase ( or state ) space endowed with a family of smooth evolution functions Φ < sup > t </ sup > that for any element of t ∈ T, the time, map a point of the phase space back into the phase space.
There are several choices for the set T. When T is taken to be the reals, the dynamical system is called a flow ; and if T is restricted to the non-negative reals, then the dynamical system is a semi-flow.
When T is taken to be the integers, it is a cascade or a map ; and the restriction to the non-negative integers is a semi-cascade.
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