Daniel Peralta-Salas (ICMAT, Madrid) Obstructions to topological relaxation for generic magnetic fields

Magnetic relaxation is a mechanism that aims to obtain magnetohydrostatic (MHS) equilibria as long-time limits of a topology-preserving evolution equation, hopefully easier to analyze that the original ideal MHD equations. My goal in this talk is to present a new theorem, in collaboration with A. Enciso, on generic obstructions for a divergence-free vector field to be topologically equivalent to some MHS equilibrium. Specifically, I will show
that for any axisymmetric toroidal domain there is a locally generic set of divergence-free vector fields that are not topologically equivalent to any smooth MHS equilibrium. Each vector field in this set is Morse-Smale on the boundary,
does not admit a nonconstant first integral, and exhibits fast growth of periodic orbits; in particular this set is residual in the Newhouse domain.