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General properties of twist maps. (Propriétés générales des applications déviant la verticale.) (French) Zbl 0714.58032
The question of existence and properties of invariant sets for twist-maps of the cylinder has a long history, and an extensive theory goes back to Birkhoff. The author proves many results analogous to those provided by the classical theory, but he does not make assumptions about the relation of the map to the Lebesgue measure. He gives criteria for existence of Aubry-Mather sets. Sets analogous to Birkhoff attractors first studied in dissipative maps are considered. Finally, a theorem about stability of the rotation interval is given. In his proofs, the author relies solely on topological methods.
Reviewer: G.Swiatek

MSC:
37E40 Dynamical aspects of twist maps
37E45 Rotation numbers and vectors
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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