Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface
Annales de l'Institut Fourier, Volume 43 (1993) no. 1, pp. 265-278.

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.

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.

     author = {Langevin, R\'emi},
     title = {Quelques nouveaux invariants des diff\'eomorphismes {Morse--Smale} d'une surface},
     journal = {Annales de l'Institut Fourier},
     pages = {265--278},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {1},
     year = {1993},
     doi = {10.5802/aif.1330},
     zbl = {0769.58033},
     mrnumber = {95g:58121},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1330/}
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Langevin, Rémi. Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface. Annales de l'Institut Fourier, Volume 43 (1993) no. 1, pp. 265-278. doi : 10.5802/aif.1330. https://aif.centre-mersenne.org/articles/10.5802/aif.1330/

[AG] S.Kh. Aranson and V.Z. Grines, The topological classification of cascades on closed two dimensional manifolds, Uspekhi Mat. Nauk, 41, 1 (1990), 3-32. | MR | Zbl

[BG] A.N. Bezdenezhnykh and V.Z. Grines, Diffeomorphisms with orientable heteroclinic sets on two-dimensional manifolds, Methods of the quantitative theory of differential equations, Gorkii State University, Gorkii (1985), 139-152.

[CL] A. Cascon et R. Langevin, A labyrinth and other ways to lose one's way. Proceedings Heraklion. Singularities and dynamical systems S.N. Pnevmatikos (editor), Elsevier Science Published B.V, North Holland, 1985.

[Fl] Fleitas. Classification of gradient like flows in dimension two and three, Bol. Soc. Bras. Math., (1975), 155-183. | MR | Zbl

[F] D. Fried, Entropy and twisted cohomology, Topology, Vol. 25 n° 4 (1986), 455-470. | MR | Zbl

[L] R. Langevin, Motifs des difféomorphismes en dimension 2, Manuscrit 1992.

[Pa] J. Palis, On Morse-Smale dynamical systems, Topology, Vol. 8, 385-404. | MR | Zbl

[PaM] J. Palis and W. De Melo, Geometric theory of dynamical systems. An introduction, Springer, New York, 1982. | MR | Zbl

[Pe1] M. Peixoto, Structural stability on two manifolds, Topology, 1 (1962), 101-120. | MR | Zbl

[Pe2] M. Peixoto, On the classification of flows on 2-manifolds, Proc. Symp. Dyn. Systems Salvador. Acad. Press, 1973, 389-419. | MR | Zbl

[SS] M. Shub and D. Sullivan, Homology theory and dynamical systems, Topology, 14 (1975), 109-132. | MR | Zbl

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