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On the complexification of real-analytic polynomial mappings of ℝ²

Ewa Ligocka (2006)

Annales Polonici Mathematici

We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.

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