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326,254
POLYNOMIAL MAPS OF AFFINE QUADRICS
"... Since the article [3] on polynomial maps of spheres appeared about 25 years ago, there have been a number of papers on the theory of rational maps of real varieties (see the references in [2], for example) which have many interesting things to say about the representation of homotopy classes by alge ..."
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Cited by 4 (0 self)
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Since the article [3] on polynomial maps of spheres appeared about 25 years ago, there have been a number of papers on the theory of rational maps of real varieties (see the references in [2], for example) which have many interesting things to say about the representation of homotopy classes
Unfolding polynomial maps at infinity
"... Let f: C n → C be a polynomial map. The polynomial describes a family of complex affine hypersurfaces f −1 (c), c ∈ C. The family is locally trivial, so the hypersurfaces have constant topology, except at finitely many irregular fibers f −1 (c) whose topology may differ from the generic or regular f ..."
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Cited by 10 (3 self)
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Let f: C n → C be a polynomial map. The polynomial describes a family of complex affine hypersurfaces f −1 (c), c ∈ C. The family is locally trivial, so the hypersurfaces have constant topology, except at finitely many irregular fibers f −1 (c) whose topology may differ from the generic or regular
Moduli space of polynomial maps
"... In the study of the dynamics of a polynomial map $f $ , the eigenvalues of the fixed points of $f $ play a very important role to characterize the original map $f $. In this paper, we shall study how many affine conjugacy classes of polynomial maps are there when the eigenvalues of their fixed point ..."
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In the study of the dynamics of a polynomial map $f $ , the eigenvalues of the fixed points of $f $ play a very important role to characterize the original map $f $. In this paper, we shall study how many affine conjugacy classes of polynomial maps are there when the eigenvalues of their fixed
POLYNOMIAL MAP SYMPLECTIC ALGORITHM
, 2002
"... Longterm stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic ..."
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Longterm stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic
NONCOMMUTATIVE POLYNOMIAL MAPS
"... Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudolinear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ is the Frobeni ..."
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Cited by 3 (0 self)
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Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudolinear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ
On Approximating the Entropy of Polynomial Mappings
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 160 (2010)
, 2010
"... We investigate the complexity of the following computational problem: Polynomial Entropy Approximation (PEA): Given a lowdegree polynomial mapping p: F n → F m, where F is a finite field, approximate the output entropy H(p(Un)), where Un is the uniform distribution on F n and H may be any of severa ..."
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We investigate the complexity of the following computational problem: Polynomial Entropy Approximation (PEA): Given a lowdegree polynomial mapping p: F n → F m, where F is a finite field, approximate the output entropy H(p(Un)), where Un is the uniform distribution on F n and H may be any
Relative cohomology of polynomial mappings
, 2008
"... Let F be a polynomial mapping from C n to C q with n> q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F −1 (∞) ”at infinity ” and its cohomology. Let us fix a weighted homogeneous degree on C[x1,...,xn] with strictly positive wei ..."
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Let F be a polynomial mapping from C n to C q with n> q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F −1 (∞) ”at infinity ” and its cohomology. Let us fix a weighted homogeneous degree on C[x1,...,xn] with strictly positive
Generalizations of Chebyshev polynomials and Polynomial Mappings
, 2004
"... In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [−1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which ..."
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In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [−1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which
An Inequality for Polynomial Mappings
 Bull. Ac. Pol.: Math
, 1992
"... Abstract. We give an estimate of the growth of a polynonial mapping of C n. 1. Main result. Let F = (F1,...,Fn) : Cn → Cn be a polynomial mapping. We put d(F) = #F −1 (w) for almost all w ∈ Cn and call d(F) the geometric degree of F. Let di = deg Fi for i = 1,...,n. Then 0 ≤ d(F) ≤ ∏n i=1 di if Fi ..."
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Abstract. We give an estimate of the growth of a polynonial mapping of C n. 1. Main result. Let F = (F1,...,Fn) : Cn → Cn be a polynomial mapping. We put d(F) = #F −1 (w) for almost all w ∈ Cn and call d(F) the geometric degree of F. Let di = deg Fi for i = 1,...,n. Then 0 ≤ d(F) ≤ ∏n i=1 di
A Geometry Of Real Polynomial Mappings
, 1999
"... In this paper we study the set of points at which a real polynomial mapping is not proper. 1 Introduction Let f : X ! Y be a continuous map of locally compact spaces. We say that the mapping f is not proper at a point y 2 Y , if there is no a neighborhood U of a point y such that the set f \Gamm ..."
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In this paper we study the set of points at which a real polynomial mapping is not proper. 1 Introduction Let f : X ! Y be a continuous map of locally compact spaces. We say that the mapping f is not proper at a point y 2 Y , if there is no a neighborhood U of a point y such that the set f
Results 1  10
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326,254