Displaying similar documents to “On the complexification of real-analytic polynomial mappings of ℝ²”

On ramification locus of a polynomial mapping

Zbigniew Jelonek (2003)

Banach Center Publications

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Let X be a smooth algebraic hypersurface in ℂⁿ. There is a proper polynomial mapping F: ℂⁿ → ℂⁿ, such that the set of ramification values of F contains the hypersurface X.

On the dynamics of extendable polynomial endomorphisms of ℝ²

Ewa Ligocka (2007)

Annales Polonici Mathematici

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We extend the results obtained in our previous paper, concerning quasiregular polynomials of algebraic degree two, to the case of polynomial endomorphisms of ℝ² whose algebraic degree is equal to their topological degree. We also deal with some other classes of polynomial endomorphisms extendable to ℂℙ².

On the extendability of quadratic polynomial mappings of the plane

Ewa Ligocka (2009)

Annales Polonici Mathematici

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We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.