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Infinite iterated function systems with overlaps

  • SZE-MAN NGAI (a1) (a2) and JI-XI TONG (a3)

Abstract

We formulate two natural but different extensions of the weak separation condition to infinite iterated function systems of conformal contractions with overlaps, and study the associated topological pressure functions. We obtain a formula for the Hausdorff dimension of the limit sets under these weak separation conditions.

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[1]Deng, Q.-R. and Ngai, S.-M.. Conformal iterated function systems with overlaps. Dyn. Syst. 26 (2011), 103123.
[2]Falconer, K. J.. The Geometry of Fractal Sets (Cambridge Tracts in Mathematics, 85). Cambridge University Press, Cambridge, 1986.
[3]Falconer, K. J.. Fractal geometry. Mathematical Foundations and Applications, 2nd edn. John Wiley & Sons, Inc., Hoboken, NJ, 2003.
[4]Fan, A. H. and Lau, K.-S.. Iterated function system and Ruelle operator. J. Math. Anal. Appl. 231 (1999), 319344.
[5]Fernau, H.. Infinite iterated function systems. Math. Nachr. 170 (1994), 7991.
[6]Hutchinson, J. E.. Fractals and self-similarity. Indiana Univ. Math. J. 30 (1981), 713747.
[7]Käenmäki, A. and Reeve, W. J.. Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets. J. Fractal Geom. 1 (2014), 83152.
[8]Lau, K.-S. and Ngai, S.-M.. Multifractal measures and a weak separation condition. Adv. Math. 141 (1999), 4596.
[9]Lau, K.-S. and Ngai, S.-M.. A generalized finite type condition for iterated function systems. Adv. Math. 208 (2007), 647671.
[10]Lau, K.-S., Ngai, S.-M. and Wang, X.-Y.. Separation conditions for conformal iterated function systems. Monatsh. Math. 156 (2009), 325355.
[11]Mauldin, R. D. and Urbański, M.. Dimensions and measures in infinite iterated function systems. Proc. London Math. Soc. (3) 73 (1996), 105154.
[12]Moran, M.. Hausdorff measure of infinitely generated self-similar sets. Monatsh. Math. 122 (1996), 387399.
[13]Ngai, S.-M. and Wang, Y.. Hausdorff dimension of self-similar sets with overlaps. J. London Math. Soc. (2) 63 (2001), 655672.
[14]Szarek, T. and Wedrychowicz, S.. The OSC does not imply the SOSC for infinite iterated function systems. Proc. Amer. Math. Soc. 133 (2005), 437440.
[15]Zerner, M. P. W.. Weak separation properties for self-similar sets. Proc. Amer. Math. Soc. 124 (1996), 35293539.

Infinite iterated function systems with overlaps

  • SZE-MAN NGAI (a1) (a2) and JI-XI TONG (a3)

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