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Matrices over a semiring of binary relations and V-variable fractals

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Abstract

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.

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References

  1. J. Hutchinson, “Fractals and Self Similarity,” Indiana Univ. Math. J. 30(5), 713–747 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Crownover, Introduction to Fractals and Chaos (Jones and Barlett Publishers, Boston-London, 1999; Postmarket, Moscow, 2000).

    Google Scholar 

  3. K. Igudesman, “Lacunary Self-Similar Fractal Sets and Intersection of Cantor Sets,” Lobachevskii J. Math. 12, 41–50 (2003).

    MathSciNet  MATH  Google Scholar 

  4. R. D. Mauldin and S. C. Williams, “Random Recursive Constructions: Asymptotic Geometric and Topological Properties,” Trans. Amer. Math. Soc. 295, 325–346 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  5. R. D. Mauldin and S. C. Williams, “Hausdorff Dimension in Graph Directed Constructions,” Trans. Amer. Math. Soc. 309(2), 811–829 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Barnsley, Superfractals (Cambridge University Press, Cambridge, 2006).

    MATH  Google Scholar 

  7. R. McGehee, “Attractors for Closed Relations on Compact Hausdorff Spaces,” Indiana Univ. Math. J. 41(4), 1165–1209 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. McGehee and T. Wiandt, “Conley Decomposition for Closed Relations,” J. Difference Equat. Appl. 12(1), 1–47 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  9. J. S. Golan, Semirings and their applications (Kluwer Academic Publishers, Dordrecht, 1999).

    MATH  Google Scholar 

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Correspondence to D. S. Biserov.

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Original Russian Text © D.S. Biserov and K.B. Igudesman, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 5, pp. 75–79.

Submitted by V.V. Shurygin

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Biserov, D.S., Igudesman, K.B. Matrices over a semiring of binary relations and V-variable fractals. Russ Math. 55, 63–66 (2011). https://doi.org/10.3103/S1066369X11050100

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  • DOI: https://doi.org/10.3103/S1066369X11050100

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