On heteroclinic separators of magnetic fields in electrically conducting fluids

• We partly solve the problem of existence of separators of a magnetic field in plasma.
• We suggest a method for studying plasma movements of special kind.
• We prove the existence of null points of a magnetic field in plasma under certain conditions.

In this paper we partly solve the problem of existence of separators of a magnetic field in plasma. We single out in plasma a 3-body with a boundary in which the movement of plasma is of special kind which we call an (a–d)-motion. We prove that if the body is the 3-annulus or the “fat” orientable surface with two holes then the magnetic field necessarily has a heteroclinic separator. The statement of the problem and the suggested method for its solution lead to some theoretical problems from Dynamical Systems Theory which are of interest of their own.