A new sufficient condition in order that the real Jacobian conjecture in R2 holds

Jaume Giné; Jaume Llibre

doi:10.1016/j.jde.2021.01.038

A new sufficient condition in order that the real Jacobian conjecture in R² holds

Jaume Giné^*, Jaume Llibre

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

Universitat de Lleida (UdL)

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

6 Cites (Scopus)

Resum

Let F=(f,g):R²→R² be a polynomial map such that det⁡(DF(x,y)) is nowhere zero and F(0,0)=(0,0). In this work we give a new sufficient condition for the injectivity of F. We also state a conjecture when det⁡(DF(x,y))= constant ≠0 and F(0,0)=(0,0) equivalent to the Jacobian conjecture.

Idioma original	Anglès
Pàgines (de-a)	333-340
Nombre de pàgines	8
Revista	Journal of differential equations
Volum	281
DOIs	https://doi.org/10.1016/j.jde.2021.01.038
Estat de la publicació	Publicada - 25 d’abr. 2021

Accés al document

10.1016/j.jde.2021.01.038

https://ddd.uab.cat/record/239777

Altres arxius i enllaços

Link to publication in Scopus

Com citar-ho

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title = "A new sufficient condition in order that the real Jacobian conjecture in R2 holds",

abstract = "Let F=(f,g):R2→R2 be a polynomial map such that det⁡(DF(x,y)) is nowhere zero and F(0,0)=(0,0). In this work we give a new sufficient condition for the injectivity of F. We also state a conjecture when det⁡(DF(x,y))= constant ≠0 and F(0,0)=(0,0) equivalent to the Jacobian conjecture.",

keywords = "Center, Global injectivity, Real Jacobian conjecture",

author = "Jaume Gin{\'e} and Jaume Llibre",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = apr,

day = "25",

doi = "10.1016/j.jde.2021.01.038",

language = "English",

volume = "281",

pages = "333--340",

journal = "Journal of differential equations",

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T1 - A new sufficient condition in order that the real Jacobian conjecture in R2 holds

AU - Giné, Jaume

AU - Llibre, Jaume

PY - 2021/4/25

Y1 - 2021/4/25

N2 - Let F=(f,g):R2→R2 be a polynomial map such that det⁡(DF(x,y)) is nowhere zero and F(0,0)=(0,0). In this work we give a new sufficient condition for the injectivity of F. We also state a conjecture when det⁡(DF(x,y))= constant ≠0 and F(0,0)=(0,0) equivalent to the Jacobian conjecture.

AB - Let F=(f,g):R2→R2 be a polynomial map such that det⁡(DF(x,y)) is nowhere zero and F(0,0)=(0,0). In this work we give a new sufficient condition for the injectivity of F. We also state a conjecture when det⁡(DF(x,y))= constant ≠0 and F(0,0)=(0,0) equivalent to the Jacobian conjecture.

KW - Center

KW - Global injectivity

KW - Real Jacobian conjecture

UR - https://www.scopus.com/pages/publications/85100466499

U2 - 10.1016/j.jde.2021.01.038

DO - 10.1016/j.jde.2021.01.038

M3 - Article

AN - SCOPUS:85100466499

SN - 0022-0396

VL - 281

SP - 333

EP - 340

JO - Journal of differential equations

JF - Journal of differential equations