A Dynamical Decomposition Theorem |
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Authors: | J. M. Aarts R. J. Fokkink J. Vermeer |
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Affiliation: | 12. Faculty of Mathematics and Informatics, Technical University Delft, P.O.BOX 5031, 2600 GA, Delft, The Netherlands
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Abstract: | By the decomposition theorem dim X ≦ n if and only if X admits a decomposition into n+1 zero-dimensional subspaces Z i for i = 0,... n. If f: X → X is a homeomorphism, then under some dimensional restrictions on the set of periodic points, the Z i can be chosen to be images of Z 0 under iterates of f. |
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