Multi-dimensional case of the problem of von Neumann–Ulam

The present report is devoted to the investigation of the multi-dimensional case of the problem of von Neumann–Ulam. We investigate the properties of Julia and Mandelbrot sets for the two-dimensional case of the famous mapping on the plane to itself. Julia and Mandelbrot sets help to define asymptotical behavior of the trajectories of certain mappings. The analytical solutions of the equations for finding fixed and periodic points and the computational simulations for describing Julia and Mandelbrot sets are the main results of this report.