Have a personal or library account? Click to login
Arcwise connected attractors of infinite iterated function systems Cover
By: Dan Dumitru  
Open Access
|Oct 2015

References

  1. [1] M.F. Barnsley, Fractals everywhere, Academic Press Professional, Boston, 1993.
  2. [2] I. Chiţescu, R. Miculescu, Approximation of fractals generated by Fredholm integral equations, J. Comput. Anal. Appl., Volume 11(2009), No. 2, 286-293.
  3. [3] D. Dumitru, Topological properties of the attractors of iterated function systems, An. Şt. Univ. Ovidius Constanţa, Vol. 19(3), 2011, 117-126.
  4. [4] R. Engelking, General topology, Polish Scientific Publishers.
  5. [5] K.J. Falconer, The geometry of fractal sets, Cambridge University Press, Cambridge, 1986.10.1017/CBO9780511623738
  6. [6] M. Hata, On the structure of self-similar sets, Japan J. Appl. Math., 2(1985), 381-414.10.1007/BF03167083
  7. [7] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30(1981), No. 5, 713-747.
  8. [8] J. Jachymski, G. Gwóźdź-Lukawska, The Hutchinson theory for infinite iterated function systems, Bull. Austral. Math. Soc., 72(2005), 441-454.10.1017/S0004972700035267
  9. [9] B. Kieninger, Iterated function systems on compact Hausdor spaces, Ph.D. Thesis, Berichte aus der Mathematik, Shaker-Verlag, Aachen 2002.
  10. [10] J. Kigami, Analysis on fractals, Cambridge univ. Press, 2001.10.1017/CBO9780511470943
  11. [11] M. Kwiecinski, A locally connected continuum which is not an IFS attractor, IMUJ Preprint, 1998/14.
  12. [12] A. Lasota, J. Myjak, Attractors of multifunctions, Bull. Pol. Ac. Sci.: Math., 48(2000), 319-334.
  13. [13] K. Leśniak, Infinite iterated function systems: a multivalued approach, Bull. Pol. Acad. Sci. Math., 52(2004), No. 1, 1-8.
  14. [14] K. Leśniak, Fixed points of the Barnsley-Hutchinson operators induced by hypercondensing maps, Le Matematiche, Vol. LX(2005), fasc. I, 67-80.
  15. [15] L. Máté, The Hutchinson-Barnsley theory for certain noncontraction mappings, Period. Math. Hungar., 27, No. 1, 1993, 21-33.10.1007/BF01877158
  16. [16] R. D. Mauldin, M. Urbański, Dimensions and measures in infinite iterated function systems, Proc. London Math. Soc., (3) 73(1996), 105-154.10.1112/plms/s3-73.1.105
  17. [17] R. D. Mauldin, M. Urbański, On the uniqueness of the density for the invatiant measure in an infinite hyperbolic iterated function system, Periodica Math. Hungarica, 37(1998), 47-53.10.1023/A:1004774202289
  18. [18] R. Miculescu, A. Mihail, Lipscomb’s space ωA is the attractor of an infinite IFS containing a ne transformations of l2(A), Proc. Amer. Math. Soc., 136(2008), 587-592.10.1090/S0002-9939-07-08981-2
  19. [19] R. Miculescu, A. Mihail, The shift space for an infinite iterated function system, Math. Rep., 11(61)(2009), No. 1, 21-32.
  20. [20] R. Miculescu, A. Mihail, Lipscomb’s L(A) space fractalized in lp(A), Mediterranean Journal of Mathematics, doi:10.1007/s00009-011-0133-9, 2011, 1-10.10.1007/s00009-011-0133-9
  21. [21] K. R. Wicks, Fractals and Hyperspaces, LNM 1492, Springer-Verlag, Berlin, 1991.10.1007/BFb0089156
DOI: https://doi.org/10.2478/auom-2014-0034 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 91 - 98
Submitted on: Dec 1, 2012
Accepted on: Mar 1, 2013
Published on: Oct 20, 2015
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2015 Dan Dumitru, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.