On Symmetry Properties of Quaternionic Analogs of Julia Sets

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dc.creatorBogush, A. A.
dc.creatorGazizov, A. Z.
dc.creatorKurochkin, Yu. A.
dc.creatorStosui, V. T.
dc.date2001-05-26
dc.date.accessioned2026-07-07T05:33:31Z
dc.date.available2026-07-07T05:33:31Z
dc.descriptionBy means of theory group analysis, some algebraic and geometrical properties of quaternion analogs of \emph{Julia} sets are investigated. We argue that symmetries, intrinsic to quaternions, give rise to the class of identical \emph{Julia} sets, which does not exist in complex number case. In the case of quadratic quaternionic mapping $X_{k+1} = X_k^2 + C$ these symmetries mean, that the shape of fractal \emph{Julia} set is completely defined by just two numbers, $C_0$ and $|{\bf C}|$. Moreover, for given $C_0$ the vector part of the \emph{Julia} set may be obtained by rotation of a two-dimensional \emph{Julia} subset of arbitrary plane, comprising ${\bf C}$, around the axis ${\bf n} = {\bf C}/|{\bf C}|$.
dc.description9 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/nlin/0105060
dc.identifierhttp://arxiv.org/abs/nlin/0105060
dc.identifierIn Proceedings of 9th Annual Seminar NPCS-2000, Minsk, Belarus (edt.'s L. Babichev and V. Kuvshivov) (2000) p. 304-309
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80020
dc.subjectChaotic Dynamics
dc.titleOn Symmetry Properties of Quaternionic Analogs of Julia Sets
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