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Jordan, Thomas; Pollicott, Mark (2006)
Publisher: Cambridge University Press
Languages: English
Types: Article
Subjects: QA

Classified by OpenAIRE into

arxiv: Mathematics::General Topology
In this paper we study certain conformal iterated function schemes in two dimensions that are natural generalizations of the Sierpinski carpet construction. In particular, we consider scaling factors for which the open set condition fails. For such ‘fat Sierpinski carpets’ we study the range of parameters for which the dimension of the set is exactly known, or for which the set has positive measure.
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    • [1] [2] [3] [4] L. M. Abramov and V. A. Rohlin. The entropy of a skew product of measure preserving transformations.
    • Trans. Amer. Math. Soc. (2) 48 (1966), 255-265.
    • C. Bishop. Topics in real analysis (unpublished lecture notes) http://www.math.sunysb.edu/∼bishop/classes/math639.S01/math639.html T. Bogenschu¨tz and H. Crauel. The Abramov-Rokhlin Formula (Lecture Notes in Mathematics, 1514).
    • Springer, Berlin, 1992, 32-35.
    • Available at: http://www.ma.umist.edu/∼nikita/gold-final.pdf K. Falconer. Fractal Geometry. Wiley, London, 1990.
    • Math. 173 (2002), 113-131.
    • [19] [20] [21] T. Jordan. Dimension of Fat Sierpinski gaskets. Preprint. Available at: http://www.maths.warwick.ac.uk/∼tjordan/overlapgasket.pdf.
    • F. Ledrappier and L.-S. Young. The metric entropy of diffeomorphisms. II. Relations between entropy, exponents and dimension. Ann. of Math. (2) 112 (1985), 540-574.
    • Math. Soc. 16 (1977), 568-576.
    • C. McMullen. The Hausdorff dimension of general Sierpinski carpets. Nagoya Math. J. 96 (1984), 1-9.
    • Soc. 350 (1998), 4065-4087.
    • Y. Peres and B. Solomyak. Problems on self-similar and self-affine sets; an update. Progr. Probab. 46 (2000), 95-106.
    • K. Petersen. Ergodic Theory. Cambridge University Press, Cambridge, 1983.
    • Math. Soc. 347 (1995), 967-983.
    • V. Rohlin. Lectures on the entropy theory of measure preserving transformations. Russian Math. Surveys 22(5) (1967), 1-52.
    • V. Rohlin. On the fundamental ideas of measure theory. Trans. Amer. Math. Soc. 71 (1952), 1-54.
    • K. Simon and B. Solomyak. On the dimension of self-similar sets. Fractals 10 (2003), 59-65.
    • K. Simon, B. Solomyak and M. Urbanski. Invariant measures for parabolic IFS with overlaps and random continued fractions. Trans. Amer. Math. Soc. 353 (2001), 5145-5164.
    • B. Solomyak. On the random series ±λn (an Erdo¨s problem). Ann. of Math. (2) 142 (1995), 611-625.
    • P. Walters. Ergodic Theory. Springer, Berlin, 1982.
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