scholarly journals Polynomial Automorphisms and the Jacobian Conjecture

2021 ◽  
Author(s):  
Arno van den Essen ◽  
Shigeru Kuroda ◽  
Anthony J. Crachiola
Keyword(s):  
Jacobian Conjecture ◽  
Polynomial Automorphisms

Polynomial remainders and plane automorphisms

2003 ◽  
Vol 68 (1) ◽  
pp. 73-79
Author(s):  
Takis Sakkalis
Keyword(s):  
Jacobian Conjecture ◽  
Real Polynomial ◽  
Polynomial Automorphisms ◽  
Polynomial Map

This note relates polynomial remainders with polynomial automorphisms of the plane. It also formulates a conjecture, equivalent to the famous Jacobian Conjecture. The latter provides an algorithm for checking when a polynomial map is an automorphism. In addition, a criterion is presented for a real polynomial map to be bijective.

scholarly journals Analytic Automorphisms and Transitivity of Analytic Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2179
Author(s):  
Zoriana Novosad ◽  
Andriy Zagorodnyuk
Keyword(s):  
Composition Operators ◽  
Jacobian Conjecture ◽  
Vector Spaces ◽  
Symmetric Polynomials ◽  
Natural Analogue ◽  
Analytic Operator ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Polynomial Automorphisms ◽  
Linear And Nonlinear

In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms that show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator that is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclicity of composition operators.

scholarly journals Analytic Automorphisms and Transitivity of Analytic Mappings

2020 ◽  
Author(s):  
Zoriana Novosad ◽  
Andriy Zagorodnyuk
Keyword(s):  
Composition Operators ◽  
Jacobian Conjecture ◽  
Vector Spaces ◽  
Symmetric Polynomials ◽  
Natural Analogue ◽  
Analytic Operator ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Polynomial Automorphisms ◽  
Linear And Nonlinear

In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.

Ont he monodromy representation of polynomial maps in n variables

2002 ◽  
Vol 39 (3-4) ◽  
pp. 361-367
Author(s):  
A. Némethi ◽  
I. Sigray
Keyword(s):  
Cohomology Group ◽  
Jacobian Conjecture ◽  
Natural Basis ◽  
Generic Fiber ◽  
Monodromy Representation ◽  
Polynomial Maps ◽  
Polynomial Map

For a   non-constant polynomial map f: Cn?Cn-1 we consider the monodromy representation on the cohomology group of its generic fiber. The main result of the paper determines its dimension and provides a natural basis for it. This generalizes the corresponding results of [2] or [10], where the case n=2 is solved. As  applications,  we verify the Jacobian conjecture for (f,g) when the generic fiber of f is either rational or elliptic. These are generalizations of the corresponding results of [5], [7], [8], [11] and [12], where the case  n=2 is treated.

A closing lemma for polynomial automorphisms of C²

Astérisque ◽  
2020 ◽  
Vol 415 ◽  
pp. 35-43
Author(s):  
Romain DUJARDIN
Keyword(s):  
Closing Lemma ◽  
Polynomial Automorphisms

scholarly journals Polynomial Retracts and the Jacobian Conjecture

1999 ◽  
Vol 352 (1) ◽  
pp. 477-484 ◽  
Author(s):  
Vladimir Shpilrain ◽  
Jie-Tai Yu
Keyword(s):  
Jacobian Conjecture
Sign in / Sign up

Export Citation Format

Share Document