A dynamical decomposition theorem

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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Authors and Affiliations

1. Faculty of Mathematics and Informatics, Technical University Delft, P.O.BOX 5031, 2600 GA, Delft, The Netherlands

   J. M. Aarts,��R. J. Fokkink & J. Vermeer

Authors

1. J. M. Aarts
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2. R. J. Fokkink
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3. J. Vermeer
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Correspondence to J. M. Aarts.

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Aarts, J.M., Fokkink, R.J. & Vermeer, J. A dynamical decomposition theorem. Acta Math Hung 94, 191–196 (2002). https://doi.org/10.1007/s10474-002-0002-7

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• Received: 10 March 2000

• Revised: 14 March 2001

• Published: 06 March 2013

• Issue Date: June 2002

• DOI: https://doi.org/10.1007/s10474-002-0002-7

Key words and phrases

• dimension
• decomposition

1991 Mathematics Subject Classification

• 54F35