Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems

Amel'kin, V. V

doi:10.31857/S0374064123030147

RAS MathematicsДифференциальные уравнения Differential Equations

ISSN (Print) 0374-0641

ISSN (Online) 3034-5030

Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems

PII

10.31857/S0374064123030147-1

DOI

10.31857/S0374064123030147

Publication type

Article

Status

Published

Authors

V. V Amel'kin

Affiliation: Belarusian State University, Minsk, 220030, Belarus

Volume/ Edition

Volume 59 / Issue number 3

Pages

432-432

Abstract

The author has retracted this article. The main results of the work, namely Theorem 1 and the corollaries arising from it, have not been strictly proven: formulas (8) are valid only under the condition . Yet, even when the indicated condition is met, formulas (9) need to be proven. Because of this, this work in its current form should be recognized as incorrect. The author is grateful to Professor L.G. Makar-Limanov, who drew attention to the lack of correct proof of formula (8) and Professor V.V. Bakhtin, who pointed to other inaccurate statements in this article.

Keywords

Date of publication

18.09.2025

Year of publication

2025

Number of purchasers

Views

References

GOST	Amel'kin V. Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems // Differential Equations. – 2023. – V. 59. – Issue number 3 C. 432-432 . URL: https://differeqras.ru/10-31857-s0374064123030147-1/?version_id=112257. DOI: 10.31857/S0374064123030147
MLA	Amel'kin, V. V "Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems." Differential Equations. 59.3 (2023).:432-432. DOI: 10.31857/S0374064123030147
APA	Amel'kin V. (2023). Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems. Differential Equations. vol. 59, no. 3, pp.432-432 DOI: 10.31857/S0374064123030147

RAS MathematicsДифференциальные уравнения Differential Equations

Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems

You can

References

Indexing

RAS MathematicsДифференциальные уравнения Differential Equations

Retraction Note: Proof of the Jacobian Conjecture in the Two-Dimensional Case and Global Isochronous Centers of Polynomial Hamiltonian Differential Systems

You can

References

Indexing

Via social network