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Asymptotic links. (Enlacements asymptotiques.) (French) Zbl 0913.58003
The paper deals with four different invariants for certain diffeomorphisms and vector fields. The first two invariants are for measure preserving diffeomorphisms of $$D^2$$, which are the identity near the boundary. They were introduced by E. Calabi [Probl. Analysis Sympos. in Honor of S. Bochner, Princeton Univ. 1969, 1-26 (1970; Zbl 0209.25801)], resp. by D. Ruelle [Ann. Inst. Henri Poincaré, Phys. Théor. 42, 109-115 (1985; Zbl 0556.58026)]. The second two invariants are for certain vector fields on three-dimensional manifolds. They were first defined by V. I. Arnol’d [Sel. Math. Sov. 5, 327-345 (1986); translation from Mater. Vses. Skh. Differ. Uravn. Beskonechnym Chislom Nezavisimykh Din. Syst. Beskonechnym Chislom Stepenej Svobodny, Dilizhane, May-June 1973, Akad. Arm. SSR, Erevan, 229-256 (1974; Zbl 0623.57016)] resp. by D. Ruelle [loc. cit.].
The authors study properties of these invariants, and show relations between them. They prove that the invariants of Calabi and those of Ruelle are topological invariants.

##### MSC:
 58C25 Differentiable maps on manifolds 37C10 Dynamics induced by flows and semiflows 28D05 Measure-preserving transformations
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