Difféologie d’espaces singuliers et petits diviseurs
June 15, 1986
 
Any (R,+) principal bundle over a manifold is trivial, this is a classical result due to the contractility of R. This property is no more true in diffeology. The projection of T2 over its quotient Ta (by a line of irrational slope a) is an example of such non trivial (R,+) principal bundle. In this paper we show how the classification of (R,+) principal over Ta is related to the question of small divisors appearing in dynamics. 
Published in les Comptes Rendus de l’Académie des Sciences, Paris 1986, vol. 302, pp. 519-522.