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Regular version of the site

Article

Dynamics of one model of the fast kinematic dynamo

Journal of Physics: Conference Series. 2018. Vol. 990. P. 1-9.

We suggest a new model of the fast nondissipative kinematic dynamo which
describes the phenomenon of exponential growth of the magnetic eld caused by the motion
of the conducting medium. This phenomenon is known to occur in the evolution of magnetic
elds 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 modi cation 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.