Classification of topologically conjugate affine mappings
We consider affine mappings from $ℝ^n$ into $ℝ^n, n ≥ 1$. We prove a theorem on the topological conjugacy of an affine mapping that has at least one fixed point to the corresponding linear mapping. We give a classification, up to topological conjugacy, for affine mappings from $ℝ$ into $ℝ$ and also...
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| Date: | 2009 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2009
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3009 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider affine mappings from $ℝ^n$ into $ℝ^n, n ≥ 1$. We prove a theorem on the topological conjugacy of an affine mapping that has at least one fixed point to the corresponding linear mapping. We give a classification, up to topological conjugacy, for affine mappings from $ℝ$ into $ℝ$ and also for affine mappings from $ℝ^n$ into $ℝ^n, n > 1$, having at least one fixed point and the nonperiodic linear part. |
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