Hiroshima Mathematical Journal

Markov-self-similar sets

Yoshiki Tsujii
Source: Hiroshima Math. J. Volume 21, Number 3 (1991), 491-519.
First Page: Show Hide
Primary Subjects: 60D05
Secondary Subjects: 54E50, 54F45, 60G57
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206128717
Mathematical Reviews number (MathSciNet): MR1148991
Zentralblatt MATH identifier: 0763.28004

References

[1] T. Bedford, Ph. D. Thesis, Warwick University (1984).
[2] T. Bedford, Dimension and dynamics for fractal recurrent sets, J. London Math. Soc. (2), 33 (1986), 86-100.
Zentralblatt MATH: 0606.28004
Mathematical Reviews (MathSciNet): MR829390
[3] F. M. Dekking, Recurrent sets, Advances in Math., 44 (1982), 78-104.
Zentralblatt MATH: 0495.51017
Mathematical Reviews (MathSciNet): MR654549
[4] K. J. Falconer, The geometry of fractal sets, Cambride University Press, Cambridge, 1985.
Zentralblatt MATH: 0587.28004
Mathematical Reviews (MathSciNet): MR867284
[5] K. J. Falconer, Random fractals, Math. Proc. Camb. Phil Soc, 100 (1986), 559-582.
Zentralblatt MATH: 0623.60020
Mathematical Reviews (MathSciNet): MR857731
[6] F. R. G. Gantmacher, Theory of matrices vol. 2, Chelsea, New York, 1974.
Zentralblatt MATH: 0927.15001
[7] S. Graf, Statistically self-similar fractals, Probab. Theory Related Fields, 74 (1987), 357-392.
Zentralblatt MATH: 0591.60005
Mathematical Reviews (MathSciNet): MR873885
[8] S. Graf, R. D. Mauldin and S. C. Williams, The exact Hausdorff dimension in random recursive constructions, Mem. Amer. Math. Soc, 381 (1988).
Zentralblatt MATH: 0641.60003
Mathematical Reviews (MathSciNet): MR920961
[9] J. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
Zentralblatt MATH: 0598.28011
Mathematical Reviews (MathSciNet): MR625600
[10] R. D. Mauldin and S. C. Williams, Random recursive constructions: asymptotic geometric and topological properties, Trans. Amer. Math. Soc, 295 (1986), 325-346.
Zentralblatt MATH: 0625.54047
Mathematical Reviews (MathSciNet): MR831202
[11] P. A. D. Moran, Additive functions of intervals and Hausdorff measure, Proc Camb. Phil. Soc, 42 (1946), 15-23.
Zentralblatt MATH: 0063.04088
Mathematical Reviews (MathSciNet): MR14397
[12] S. Takahashi, Self-similarity of linear cellular automata, to appear in J. Comput. Sys. Sci.
Zentralblatt MATH: 0743.68105
Mathematical Reviews (MathSciNet): MR1161108
[13] H. Totoki and Y. Tsujii, A remark on random fractals, Hiroshima Math. J., 19 (1989), 563-566.
Zentralblatt MATH: 0702.28005
Mathematical Reviews (MathSciNet): MR1035143
[14] Y. Tsujii, Generalized random ergodic theorems and the Hausdorff-measures of random fractals, Hiroshima Math. J., 19 (1989), 363-377.
Zentralblatt MATH: 0701.60010
Mathematical Reviews (MathSciNet): MR1027940
[15] S. J. Willson, Cellular automata can generate fractals, Discrete Applied Mathematics. 8 (1984), 91-99.
Zentralblatt MATH: 0533.68051
Mathematical Reviews (MathSciNet): MR739602

2013 © Hiroshima University, Department of Mathematics

Hiroshima Mathematical Journal

Hiroshima Mathematical Journal