The paper presents an explicit formula for the number of fixed point of a C∞ map of a segment [a, b] ⊂ ℝ. While the formula can be derived from the Lefschetz fixed point theorem for general CW -complexes, the new proof is instructive and highlights the contributions of degenerate fixed points.
@article{1650,
title = {On Brouwer's Fixed Point Theorem},
journal = {CUBO, A Mathematical Journal},
volume = {6},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/1650}
}
Tarkhanov, N. On Brouwer's Fixed Point Theorem. CUBO, A Mathematical Journal, Tome 6 (2004) . http://gdmltest.u-ga.fr/item/1650/