The Exploration of Two-Dimensional Cases of Feigenbaum’s Results: The Exploration of Two-Dimensional Cases of Feigenbaum’s Results - Seytov, Sh.J.; Xudaybergenova, Gulrabo (MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 2024)
The focus of this paper is on exploring the multi-dimensional case of the results of M.Feigenbaum. Specifically, we delve into the properties of Julia and Mandelbrot sets in the context of the renowned mapping from the plane to itself in two dimensions. These sets play a crucial role in determining the asymptotic behavior of trajectories for certain mappings. The primary outcomes of this investigation include the analytical solutions derived for locating fixed and periodic points. Additionally, the paper presents computational simulations aimed at describing Julia and Mandelbrot sets.