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Some dynamical properties of\(F(z) = z^2 - 2\bar z\)

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We study in this note some dynamical properties of\(F(z) = z^2 - 2\bar z\),F:ℂ→ℂ. LetK=K (F) denote the set of all points whose orbit is bounded. We prove thatF restricted to ℂ\K behaves as ψ(z)=z 2 does in the complement of the unit disk;K has positive area;F restricted toK is transitive; the set of periodic points ofF is dense inK and the topological entropy of F/K is positive.

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Author information

Correspondence to Jefferson King-Dávalos.

Additional information

Research supported in part by PAPIIT grant IN 101700.

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King-Dávalos, J., Méndez-Lango, H. & Sienra-Loera, G. Some dynamical properties of\(F(z) = z^2 - 2\bar z\) . Qual. Th. Dyn. Syst. 5, 101–120 (2004). https://doi.org/10.1007/BF02968132

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Key words

  • Periodic points
  • transitive mapping
  • topological entropy