Finite-type invariants of magnetic lines - Akhmet'ev, Petr
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Properties of magnetic flows are described using high dimensional configuration spaces. Arnold asymptotic ergodic invariant of magnetic lines is the basic example. Asymptotic invariants of magnetic lines are related to stable homotopy groups of spheres, are detected by Postnikov k-invariants. Anosov flows on 3D homology spheres are models of stable magnetic knots. Finite-type invariants of magnetic line are required to describe properties of turbulent flows and determine constraints in magnetic feld relaxation with free boundary.

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Produktbeschreibung
Properties of magnetic flows are described using high dimensional configuration spaces. Arnold asymptotic ergodic invariant of magnetic lines is the basic example. Asymptotic invariants of magnetic lines are related to stable homotopy groups of spheres, are detected by Postnikov k-invariants. Anosov flows on 3D homology spheres are models of stable magnetic knots. Finite-type invariants of magnetic line are required to describe properties of turbulent flows and determine constraints in magnetic feld relaxation with free boundary.
Autorenporträt
2000 Steklov Institute, dissertation:"Embeddings of compacta, stable homotopy groups of spheresand singularities theory". 1989-- Pushkov Institute of Terrestrial Magnetism, Ionosphere and RadioWave Propagation (IZMIRAN), Troitsk, Russia, Leading Researcher.2015-- HSE Moscow Institute of Electronics and Mathematics (MIEM HSE), Professor.