- Tytuł:
- On the convergence of multicomplex M-J sets to the Steinmetz hypersolids
- Autorzy:
- Katunin, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/122672.pdf
- Data publikacji:
- 2016
- Wydawca:
- Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
- Tematy:
-
generalized M-J sets
multicomplex M-J sets
convergence
Steinmetz hypersolid
uogólniony zbiór Mandelbrot-Julia
analiza fraktalna
konwergencja - Opis:
- In this paper, the analysis of generalized multicomplex Mandelbrot-Julia (henceforth abbrev. M-J) sets is performed in terms of their shape when a degree of an iterated polynomial tends to infinity. Since the multicomplex algebras result from a tensor product of complex algebras, the dynamics of multicomplex systems described by iterated polynomials is different with respect to their complex and hypercomplex analogues. When the degree of an iterated polynomial tends to infinity the M-J sets tend to the higher dimensional generalization of the Steinmetz solid, depending on the dimension of a vector space, where a given generalization of M-J sets is constructed. The paper describes a case of bicomplex M-J sets with appropriate visualizations as well as a tricomplex one, and the most general case - the muticomplex M-J sets, and their corresponding geometrical convergents.
- Źródło:
-
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 67-74
2299-9965 - Pojawia się w:
- Journal of Applied Mathematics and Computational Mechanics
- Dostawca treści:
- Biblioteka Nauki
Artykuł