Nondissipativ kinematic dynamics on lenses

In the paper we construct smooth (infinitely differentiable) diffeomorphism of three dimensional lens (that is a closed three-manifold that is sheet-finitely covered by three-dimensional sphere). We include a three-dimensional sphere in the list of lens. This mapping has a positive entropy and preserves the volume in some neighborhood of its non-wandering set. We examine the space of diffeomorphisms that are conservative in some neighborhood of their non-wandering sets. In this space there is a neighbourhood consisting of mappings with positive topological entropy (i.e., the diffeomorphism constructed is relatively stable in the class of diffeomorphisms). Due to its properties, the diffeomorphism constructed can act like a model of non-dissipative kinematic fast dynamo. The question is open either the diffeomorphism constructed is the model of a middle or dissipative fast dynamo.