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Transport in Hamiltonian systems. (English) Zbl 0585.58039

The authors develop a theory of transport in Hamiltonian systems in the context of iteration of area-preserving maps. Invariant closed curves present complete barriers to transport, but in regions without such curves there are still invariant Cantor sets. In the regular components the motion is quasiperiodic and orbits lie in the KAM tori. By dividing the irregular components of phase space into regions separated by the strongest partial barriers, and assuming the motion is mixing within these regions, they present a global picture of transport.
Reviewer: W.V.Oliva

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
82C70 Transport processes in time-dependent statistical mechanics
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