The "initial conditions" in the definition refer to the given, or initial, points x and y. The definition says that f has sensitive dependence if arbitrarily close to any given point x in the domain of f there is a point and an nth iterate that is farther from the nth iterate of x than a distance Î. This has practical significance, because in such instances higher iterates of an approximate value of x may not resemble the true iterates of x.

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