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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 12, Pages 95–100 (Mi ivm6031)  
Brief communications

Systems of two iterated functions over skew field of quaternions

P. I. Troshin

Chair of Geometry, Kazan State University, Kazan, Russia
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Abstract: Systems of linear iterated functions $f_0(z)=qz+a$, $f_1(z)=qz+b$ over the field of complex numbers have been investigated since 1985 (Barnsley and Harrington). Much attention is paid to the question of the connectedness of their attractors. We consider systems of iterated functions $f_0(z)=qzp+a$, $f_1(z)=qzp+b$ over the skew field of quaternions. We simplify the form of such systems and study the structure of their attractors.
Keywords: system of iterated functions, attractor, quaternion.
Received: 04.06.2008
Revised: 11.06.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 12, Pages 81–86
DOI: https://doi.org/10.3103/S1066369X09120135
Bibliographic databases:
Document Type: Article
UDC: 514.74+517.987
Language: Russian
Citation: P. I. Troshin, “Systems of two iterated functions over skew field of quaternions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 12, 95–100; Russian Math. (Iz. VUZ), 53:12 (2009), 81–86
Citation in format AMSBIB
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\by P.~I.~Troshin
\paper Systems of two iterated functions over skew field of quaternions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 12
\pages 95--100
\mathnet{http://mi.mathnet.ru/ivm6031}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2664479}
\zmath{https://zbmath.org/?q=an:1181.30030}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 12
\pages 81--86
\crossref{https://doi.org/10.3103/S1066369X09120135}
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