Mathematics – Geometric Topology
Scientific paper
2011-05-30
Mathematics
Geometric Topology
Scientific paper
We investigate a problem by V.I.Arnol'd about higher analog of the asymptotic Hopf invariant of divergence-free vector fields. A higher invariant of magnetic fields, which is not expressed from the asymptotic linking numbers of magnetic lines is constructed and examples of an asymptotic invariants are presented. A definition of asymptotic finite-order invariant for classical links is presented. Various problems, which are investigated by means of the magnetic helicity invariant are considered.
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