On the dynamics of extendable polynomial endomorphisms of ℝ²

Ewa Ligocka

The search session has expired. Please query the service again.

Displaying similar documents to “On the dynamics of extendable polynomial endomorphisms of ℝ²”

Degrees of Polynomial Solutions of a Class of Riccati - tipe Differential Equations*.

Mira Bhargava (1964)

Collectanea Mathematica

Similarity:

Existence of Polynomial Solutions of a Class of Riccati-Type Differential Equations.

H. Kaufman, Mira Bhargava (1965)

Collectanea Mathematica

Similarity:

Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller, Artur Korniłowicz (2016)

Formalized Mathematics

Similarity:

In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.

On the complexification of real-analytic polynomial mappings of ℝ²

Ewa Ligocka (2006)

Annales Polonici Mathematici

Similarity:

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 Roots of Polynomials with Positive Coefficients

Toufik Zaïmi (2011)

Publications de l'Institut Mathématique

Similarity:

A generalization of a polynomial lemma of Leja

J. Siciak (1971)

Annales Polonici Mathematici

Similarity:

On some properties of polynomial functions

R. Ger (1971)

Annales Polonici Mathematici

Similarity:

Intersective sets given by a polynomial

Jason Lucier (2006)

Acta Arithmetica

Similarity:

On an orthonormal polynomial basis in the space C[-1,1]

Krzysztof Woźniakowski (2001)

Studia Mathematica

Similarity:

We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.

Explicit constructions of extractors and expanders

Norbert Hegyvári, François Hennecart (2009)

Acta Arithmetica

Similarity:

On the number of terms of a composite polynomial

Umberto Zannier (2007)

Acta Arithmetica

Similarity:

A formula for the supersingular polynomial

Luís R. A. Finotti (2009)

Acta Arithmetica

Similarity:

Selected Chapters from Algebra, II

I. R. Shafarevich (1999)

The Teaching of Mathematics

Similarity:

Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II.

Chistov, A.L. (2005)

Zapiski Nauchnykh Seminarov POMI

Similarity:

Local polynomials are polynomials

C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)

Studia Mathematica

Similarity:

We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.

Near solutions of polynomial equations

Shih Ping Tung (2006)

Acta Arithmetica

Similarity:

On ramification locus of a polynomial mapping

Zbigniew Jelonek (2003)

Banach Center Publications

Similarity:

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.

Plane Jacobian conjecture for simple polynomials

Nguyen Van Chau (2008)

Annales Polonici Mathematici

Similarity:

A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

Jacek Chądzyński, Tadeusz Krasiński (1992)

Annales Polonici Mathematici

Similarity:

A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.

The determinant of oriented rotants

Adam H. Piwocki (2007)

Colloquium Mathematicae

Similarity:

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