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| Polynomial Homogeneous Maps and Their Periods |
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| KeyWord:Homogeneous polynomial map Period Set of period Self-map of a sphere |
| Author Name | Affiliation | | Jaume Llibre | Departament de Matem\`{a}tiques, Universitat Aut\`{o}noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain | | Violetta Pilyugina | Departament de Matem\`{a}tiques, Universitat Aut\`{o}noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain |
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| Abstract: |
| We study the set of periods of the homogeneous polynomial maps $f:
\R^n \to \R^n$ and $f: \C^n \to \C^n$ of degree $m>1$. For these
complex maps, we also describe the number of invariant straight lines through the origin by $f^k$ for $k=1,2,\ldots$ and the dynamics of $f^k$ over them. |
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