An analytical description of mandelbrot and Julia sets for some multi-dimensional cubic mappings.

The present paper investigates the multi-dimensional case of the cubic mappings. We have investigated the properties of Mandelbrot and Julia sets for the two-dimensional case of the mappings on the plane to itself. Mandelbrot and Julia sets help to define asymptotical behavior of the trajectories. The analytical solutions of the equations for finding fixed points and the computer simulations for describing Mandelbrot and Julia sets are the main results of this paper. [ABSTRACT FROM AUTHOR]