On the topology of the potential magnetic field

The geometry of the magnetic fields in plasma plays an important role in understanding a number of fundamental problems in physics. lt is clear that the magnetic field like any vector field defines a dynamical system on some three-dimensional manifold. This idea is used by physicists for a long time (since the middle of the last century). This work is devoted to the application of methods dynamical systems to description of the patterns of magnetic fields in the solar corona. Such models correspond to a gradient-like dynamical systems for which there is a complete topological classification. It follows that magnetic field with four springs can have countable number of structurally stable configurations of the field geometry.