Homeomorphisms | Topological dynamics

Topological conjugacy

In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct of flows, are important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterative function can be determined, then that for a topologically conjugate function follows trivially. To illustrate this directly: suppose that and are iterated functions, and there exists a homeomorphism such that so that and are topologically conjugate. Then one must have and so the iterated systems are topologically conjugate as well. Here, denotes function composition. (Wikipedia).

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Topological space | Inverse function | Logistic map | Tent map | Julia set | Dynamical system | Homeomorphism | Periodic point | Hénon map | Continuous function | Injective function | Commutative diagram | Matrix similarity | Iterated function | Mathematics | Function (mathematics) | Diffeomorphism | Bijection | Equivalence relation | Jordan normal form | Flow (mathematics) | Function composition