= Deterministic evolution
{title2=$x_n=F^n(x_0)$}
Evolution is deterministic when a specified <initial condition> and evolution rule select a unique future <orbit>. For a <discrete dynamical system>, applying the same <map> to the same state gives the same next state. For an <ordinary differential equation>, uniqueness of the <initial value problem> is required; merely writing a <differential equation> does not guarantee it.
Determinism permits both <asymptotic stability> and <sensitive dependence on initial conditions>. It does not by itself imply reliable prediction from approximate measurements, and sensitivity does not introduce a random choice into the evolution rule.
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