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A generalization of mixed invariant sets

Part of: Functions of several variables

Published online by Cambridge University Press:  26 February 2010

Uwe Feiste
Uwe Feiste
Affiliation:
Ernst-Moritz-Arndt-Universität Greifswald, Sektion Mathematik, Friedrich-Ludwig-Jahn-Straβe 15a, Greifswald, DDR-2200.
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Summary

The concept of mixed invariant set is due to Bandt [1], Bedford [2], Dekking [3, 4], Marion [4] and Schulz [10]. An m-tuple B = (B1, …, Bm) of closed and bounded subsets Bi of a complete finitely compact (bounded and closed subsets are compact) metric space X is called a mixed invariant set with respect to contractions f1, …, fm and a transition matrix M = (mij), if, and only if,

for every i ∈ {1, …, m}. In the papers quoted an essential condition is that all mappings f1, …, fm be contractions. We will show that, under certain conditions, the construction of mixed invariant sets also works in cases where some of the mappings are isometries or even expanding mappings.

MSC classification

Secondary: 26B99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 198 - 206
Copyright
Copyright © University College London 1988

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References

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