Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface
Annales de l'Institut Fourier, Tome 43 (1993) no. 1, p. 265-278
Soit f un difféomorphisme Morse-Smale d’une surface fermée. À une courbe instable de comportement 1 par rapport à un attracteur A de f correspond une courbe fermée sur un des tores (Bassin(A)-A)/(f). Cette remarque nous permettra de définir de nouveaux invariants de conjugaison de f. Nous en déduisons aussi un moyen d’écrire explicitement une puissance de f comme le produit du temps 1 d’un champ de vecteurs Morse-Smale topologique par des isotopies à support des disques et des twists de Dehn de supports disjoints.
Let f be a Morse-Smale diffeomorphism of a closed surface. The image of an unstable curve of behaviour 1 with respect to an attractor A of f in (Bassin(A)-A)/(f) is a closed curve. This observation allows us to define new conjugation invariants of f. It gives also a way of explicitely decomposing a power of f as the product of the time 1 of a topological Morse-Smale vector field by isotopies supported in discs and Dehn twists with disjoint supports.
@article{AIF_1993__43_1_265_0,
     author = {Langevin, R\'emi},
     title = {Quelques nouveaux invariants des diff\'eomorphismes Morse--Smale d'une surface},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {43},
     number = {1},
     year = {1993},
     pages = {265-278},
     doi = {10.5802/aif.1330},
     zbl = {0769.58033},
     mrnumber = {95g:58121},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1993__43_1_265_0}
}
Langevin, Rémi. Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface. Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 265-278. doi : 10.5802/aif.1330. http://www.numdam.org/item/AIF_1993__43_1_265_0/

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