On \(C^{1}\) classifications of hyperbolic vector fields. (Q1406523)
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scientific article; zbMATH DE number 1974962
| Language | Label | Description | Also known as |
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| English | On \(C^{1}\) classifications of hyperbolic vector fields. |
scientific article; zbMATH DE number 1974962 |
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On \(C^{1}\) classifications of hyperbolic vector fields. (English)
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4 September 2003
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The authors consider \(n\)-dimensional systems \(\dot x= A_i x+ \text{h.o.t.}\), where the matrices \(A_i\) have no eigenvalue with zero real part. In case \(n\leq 4\), it is shown that the systems are \(C^1\) orbitally equivalent (\(C^1\) conjugate) if \(A_i\) are similar (strictly). For \(n= 5\), the same result is true if there is no multiple eigenvalue.
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conjugacy
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linearization
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resonant normal form
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vector fields
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\(C^1\) classification
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