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/