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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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