The degree at infinity of the gradient of a polynomial in two real variables
Volume 87 / 2005
Annales Polonici Mathematici 87 (2005), 229-235
MSC: 14P15, 32B10.
DOI: 10.4064/ap87-0-19
Abstract
Let $f:\mathbb{R}^2\to\mathbb{R}$ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient $\nabla f$ in terms of the real branches at infinity of the level curves $\{f(x,y)=\lambda\}$ for some $\lambda\in\mathbb{R}$. The formula obtained is a counterpart at infinity of the local formula due to Arnold.
