High Quality Content by WIKIPEDIA articles! In mathematics, two functions are said to be topologically conjugate to one another if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy is important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterated function can be solved, then those for any topologically conjugate function follow trivially.To illustrate this directly: suppose that f and g are iterated functions, and there exists an h such that g=h^{-1}circ fcirc h, so that f and g are topologically conjugate. Then of course one must have g^n=h^{-1}circ f^ncirc h, and so the iterated systems are conjugate as well. Here, circ denotes function composition.

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