Geodesic
Matrices over a~semiring of binary relations and $V$-variable fractals
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 75-79.

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In this paper we prove that $V$-variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space.
Keywords: binary relations, matrices over a semiring, iterated function systems, attractor
Mots-clés : $V$-variable fractal. 
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D. S. Biserov; K. B. Igudesman. Matrices over a~semiring of binary relations and $V$-variable fractals. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 75-79. http://geodesic.mathdoc.fr/item/IVM_2011_5_a9/

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

[2] Kronover R., Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii, Postmarket, M., 2000

[3] Igudesman K., “Lacunary self-similar fractal sets and intersection of Cantor sets”, Lobachevskii J. Math., 12 (2003), 41–50 | MR | Zbl

[4] Mauldin R. D., Williams S. C., “Random recursive constructions: asymptotic geometric and topological properties”, Trans. Amer. Math. Soc., 295 (1986), 325–346 | DOI | MR | Zbl

[5] Mauldin R. D., Williams S. C., “Hausdorff dimension in graph directed constructions”, Trans. Amer. Math. Soc., 309:2 (1988), 811–829 | DOI | MR | Zbl

[6] Barnsley M., Superfractals, Cambridge University Press, Cambridge, 2006 | MR | Zbl

[7] McGehee R., “Attractors for closed relations on compact Hausdorff spaces”, Indiana Univ. Math. J., 41:4 (1992), 1165–1209 | DOI | MR | Zbl

[8] McGehee R., Wiandt T., “{Conley decomposition for closed relations},”, J. Difference Equ. Appl., 12:1 (2006), 1–47 | DOI | MR | Zbl

[9] Golan J. S., Semirings and their applications, Kluwer Academic Publishers, Dordrecht, 1999 | MR