On One Approach to the Construction of a Non-Dissipative Kinematic Dynamo on a Non-Compact Manifold

The article discusses models of large-scale objects in which the effect of a non-dissipative kinematic dynamo takes place. A dynamo design is constructed for finite divergence-free vector fields and diffeomorphisms in n— dimensional space. The approach uses the construction of prolonging a vector field from the unit sphere to a divergence-free finite vector field in space.