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HAUSDORFF DIMENSION OF GENERALIZED MARKOV ATTRACTORS FOR ITERATED FUCTION SYSTEMS

  • Published : 2002.02.01

Abstract

We construct lots of non-self similar fractal sets called generalized Markov attractors for a given (hyperbolic) iterated function system and calculated bounds of their Hausdorff dimensions.

Keywords

attractor;Hausdorff dimension;iterated function system

References

  1. Indiana Univ. Math. J. v.30 Fractals and self-similarity J. Hutchinson https://doi.org/10.1512/iumj.1981.30.30055
  2. Math. Proc. Camb. Phil. Soc. v.110 Dimensions associated with recurrent self-similar sets A. Deliu;J. Geronimo;R. Shonkwiler https://doi.org/10.1017/S0305004100070407
  3. Non-negative matrices E. Seneta
  4. Lecture Notes in Mathematics v.1342 Non-self-similar attractors of hyperbolic iterated function systems D. Ellis;M. Branton https://doi.org/10.1007/BFb0082829
  5. Topology Proc. v.11 Hausdorff dimension J. Keesling
  6. Fractal Geometry John Wiley & Sons K. Falconer
  7. Math. Nachr. v.142 Self-similar sets, Ⅰ. Topological Markov chains and mixed self-similar sets C. Bandt https://doi.org/10.1002/mana.19891420107
  8. Mathematika v.35 A generalization of mixed invariant sets U. Feiste https://doi.org/10.1112/S0025579300015199
  9. Hiroshima Math. J. v.21 Markov-self-similar sets Y. Tsujii
  10. J. Austral. Math. Soc. (Series A) v.55 On Hausdorff dimension for attractors of iterated function systems Q. Yin https://doi.org/10.1017/S1446788700032031