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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - P. I. Troshin
TI  - Systems of two iterated functions over skew field of quaternions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 95
EP  - 100
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_12_a12/
LA  - ru
ID  - IVM_2009_12_a12
ER  - 
%0 Journal Article
%A P. I. Troshin
%T Systems of two iterated functions over skew field of quaternions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 95-100
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_12_a12/
%G ru
%F IVM_2009_12_a12
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/

[1] Barnsley M. F., Harrington A. N., “A Mandelbrot set for pairs of linear maps”, Phisica D, 15 (1985), 421–432 | MR | Zbl

[2] Bandt C., “On the Mandelbrot set for pairs of linear maps”, Nonlinearity, 15 (2002), 1127–1147 | DOI | MR | Zbl

[3] Solomyak B., “On the “Mandelbrot set” for pairs of linear maps: asymptotic self-similarity”, Nonlinearity, 18 (2005), 1927–1943 | DOI | MR | Zbl

[4] Girard P. R., Quaternions, Clifford algebras and relativistic physics, Birkhäuser, Basel–Boston–Berlin, 2007, 179 pp. | MR | Zbl

[5] Hutchinson J. E., “Fractals and similarity”, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR | Zbl

[6] Barnsley M. F., Demko S., “Iterated function systems and the global construction of fractals”, Proc. Roy. Soc. London. Ser. A, 399:1817 (1985), 243–275 | DOI | MR | Zbl