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Displaying similar documents to “On ramification locus of a polynomial mapping”

On the complexification of real-analytic polynomial mappings of ℝ²

Ewa Ligocka (2006)

Annales Polonici Mathematici

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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.

On the dynamics of extendable polynomial endomorphisms of ℝ²

Ewa Ligocka (2007)

Annales Polonici Mathematici

Similarity:

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.

The determinant of oriented rotants

Adam H. Piwocki (2007)

Colloquium Mathematicae

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We study the determinant of pairs of rotants of Anstee, Przytycki and Rolfsen. We consider various notions of rotant orientations.

A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form

Henrique Fernandes de Lima (2022)

Archivum Mathematicum

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We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].

Combinatorial Nullstellensatz approach to polynomial expansion

Fedor Petrov (2014)

Acta Arithmetica

Similarity:

Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.