Dynamics of one model of the fast kinematic dynamo

We suggest a new model of the fast nondissipative kinematic dynamo which describes the phenomenon of exponential growth of the magnetic field caused by the motion of the conducting medium. This phenomenon is known to occur in the evolution of magnetic fields of astrophysical bodies. In the 1970s A.D. Sakharov and Ya.B. Zeldovich proposed a "rope" scheme of this process which in terms of the modern theory of dynamical systems can be described as Smale solenoid. The main disadvantage of this scheme is that it is non-conservative. Our model is a modification of the Sakharov-Zeldovich's model. We apply methods of the theory of dynamical systems to prove that it is free of this fault in the neighborhood of the nonwandering set.