Geodesic
Systems of two iterated functions over skew field of quaternions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 95-100

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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
Mots-clés : quaternion. 
@article{IVM_2009_12_a12,
     author = {P. I. Troshin},
     title = {Systems of two iterated functions over skew field of quaternions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {95--100},
     publisher = {mathdoc},
     number = {12},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_12_a12/}
}
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P. I. Troshin. Systems of two iterated functions over skew field of quaternions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 95-100. http://geodesic.mathdoc.fr/item/IVM_2009_12_a12/