Abstract
This paper discusses the gap sequences of self-conformal sets satisfying the strong separation condition.
Similar content being viewed by others
References
T. Bedford Crinkly curves, Markov partitions and box dimension in self-similar sets, Ph.D. Thesis, University of Warwick, 1984.
Besicovitch A.S., Taylor S. J.: On the complementary intervals of a linear closed set of zero Lebesgue measure. J. London Math. Soc. 29, 449–459 (1954)
Falconer K.: Techniques in fractal geometry. John Wiley & Sons, Ltd., Chichester (1997)
Federer G.: Geometric measure theory. Springer, New York (1969)
Falconer K.J., Marsh D.T.: On the Lipschitz equivalence of Cantor sets. Mathematika 39, 223–233 (1992)
Garcia I., Molter U., Scotto R.: Dimension functions of Cantor sets. Proc. Amer. Math. Soc. 135(10), 3151–3161 (2007) (electronic)
McMullen C.: The Hausdorff dimension of general Sierpinski Carpets. Nagoya Math. J. 96, 1–9 (1984)
Rao H., Ruan H.J., Yang Y.M.: Gap sequence, Lipschitz equivalence and box dimension of fractal sets. Nonlinearity 21, 1339–1347 (2008)
Tricot C.: Douze définitions de la densité logarithmique. C. R. Acad. Sci. Paris, Ser. I 293, 549–552 (1981)
Xiong Y., Wu M.: Category and dimensions for cut-out sets. J. Math. Anal. Appl. 358, 125–135 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work is supported by NSFC (Nos. 11371329, 11071224, 11471124, 11301346), NCET, NSF of Zhejiang Province (Nos. LR13A1010001, LY12F02011) and the Chinese University of Hong Kong.
Rights and permissions
About this article
Cite this article
Deng, J., Wang, Q. & Xi, L. Gap sequences of self-conformal sets. Arch. Math. 104, 391–400 (2015). https://doi.org/10.1007/s00013-015-0752-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-015-0752-7