Maximal invariant compact sets of dynamical systems (Q656317)
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scientific article; zbMATH DE number 5998389
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal invariant compact sets of dynamical systems |
scientific article; zbMATH DE number 5998389 |
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Maximal invariant compact sets of dynamical systems (English)
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17 January 2012
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The paper considers a general discrete dynamical system \(x_{n+1}=F(x_n)\) defined by a continuous mapping \(F:M\to M\), where \(M\subset\mathbb R^n\). Necessary and sufficient conditions for the system to have a maximal positively invariant (negatively invariant, invariant) compact set are presented. A method for determining this set is proposed. Similar results are also obtained for a continuous dynamical system given by an autonomous differential equation \(\dot x=f(x)\), \(x\in\mathbb R^n\).
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discrete dynamical systems
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continuous dynamical systems
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maximal invariant compact sets
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positively invariant sets
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negatively invariant sets
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0.93487394
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0.9266448
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0.91978973
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0.91692847
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0.91692847
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0.91144854
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