The topological structure of attractors for differentiable functions (Q1912721)
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scientific article; zbMATH DE number 878213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The topological structure of attractors for differentiable functions |
scientific article; zbMATH DE number 878213 |
Statements
The topological structure of attractors for differentiable functions (English)
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29 October 1996
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A cleavage between the structure of \(\omega\)-limit sets for continuous functions and the structure of \(\omega\)-limit sets for Lipschitz functions described in \textit{A. M. Bruckner} and \textit{T. H. Steele} [J. Math. Anal. Appl. 188, No. 3, 798-808 (1994; Zbl 0820.26001)] rested on measure theoretic considerations. Present paper shows that the situation is different when the topological structure of these classes of \(\omega\)-limit sets is considered. It is shown that every nowhere dense compact set is homeomorphic to an \(\omega\)-limit set for a differentiable function with bounded derivative.
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homoclinic
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\(\omega\)-limit sets
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continuous functions
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Lipschitz functions
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differentiable function
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