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

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 α(y) ≡ 0. 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.