The degree at infinity of the gradient of a polynomial in two real variables
Annales Polonici Mathematici (2005)
- Volume: 87, Issue: 1, page 229-235
- ISSN: 0066-2216
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topMaciej Sękalski. "The degree at infinity of the gradient of a polynomial in two real variables." Annales Polonici Mathematici 87.1 (2005): 229-235. <http://eudml.org/doc/280505>.
@article{MaciejSękalski2005,
abstract = {Let f:ℝ² → ℝ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient ∇f in terms of the real branches at infinity of the level curves \{f(x,y) = λ\} for some λ ∈ ℝ. The formula obtained is a counterpart at infinity of the local formula due to Arnold.},
author = {Maciej Sękalski},
journal = {Annales Polonici Mathematici},
keywords = {degree at infinity; index of gradient; branch at infinity},
language = {eng},
number = {1},
pages = {229-235},
title = {The degree at infinity of the gradient of a polynomial in two real variables},
url = {http://eudml.org/doc/280505},
volume = {87},
year = {2005},
}
TY - JOUR
AU - Maciej Sękalski
TI - The degree at infinity of the gradient of a polynomial in two real variables
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 229
EP - 235
AB - Let f:ℝ² → ℝ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient ∇f in terms of the real branches at infinity of the level curves {f(x,y) = λ} for some λ ∈ ℝ. The formula obtained is a counterpart at infinity of the local formula due to Arnold.
LA - eng
KW - degree at infinity; index of gradient; branch at infinity
UR - http://eudml.org/doc/280505
ER -
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