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1	A Combinatorial Analog of the Poincaré–Birkhoff Fixed Point Theorem Cloutier, John 01 May 2003 (has links) Results from combinatorial topology have shown that certain combinatorial lemmas are equivalent to certain topologocal fixed point theorems. For example, Sperner’s lemma about labelings of triangulated simplices is equivalent to the fixed point theorem of Brouwer. Moreover, since Sperner’s lemma has a constructive proof, its equivalence to the Brouwer fixed point theorem provides a constructive method for actually finding the fixed points rather than just stating their existence. The goal of this research project is to develop a combinatorial analogue for the Poincare ́-Birkhoff fixed point theorem. Fixed Point Theorem Poincare ́-Birkhoff Combinatorial Analogue
2	A la recherche des tores perdus Nguyen, Tien Zung 23 November 2001 (has links) (PDF) C'est l'histoire d'un mathématicien qui est allé à la recherche des tores perdus<br />dans la jungle des systèmes complètement intégrables. Il a trouvé des feuilles<br />particulières et des tores pour construire une petite cabane qui donne une vue<br />topologique sur la jungle. [MATH] Mathematics actions toriques système integrable forme normale de poincare-Birkhoff monodromie arnold-liouville avec singularites classification topologique structure affine stratifiee