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Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Tuesday, July 20, 16:00 ~ 16:50 UTC-3

On the Jacobian conjecture in $\mathbb{R}^2$ and its relations with the global centers of $\mathbb{R}^2$

Jaume Llibre

Universitat Autònoma de Barcelona, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $F = (f,g):\mathbb{R}^2\to\mathbb{R}^2$ be a polynomial map such that the Jacobian $\det DF(p)$ is different from zero for all $p\in\mathbb{R}^2$. The real Jacobian conjecture is about the injectivity of $F$. While the Jacobian conjecture assumes that $\det DF(p)$ is a constant different from zero and claims that the map $F$ is injective. This talk presents a survey on these conjectures and their relations with the global centers in $\mathbb{R}^2$.

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