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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 NameAffiliation
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.