论文信息 - On the Hausdorff dimension of Cantor-like sets with overlaps - 字舞流文

On the Hausdorff dimension of Cantor-like sets with overlaps

Abstract We give a lower estimate of the Hausdorff dimension for Cantor-like sets which are obtained by an overlapping Moran-like construction.

Tomasz Szarek | J. Myjak | T. Szarek | Józef Myjak

[1] J. Myjak,et al. A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps , 2001 .

[2] Y. Pesin,et al. Dimension theory in dynamical systems , 1997 .

[3] P. A. P. Moran,et al. Additive functions of intervals and Hausdorff measure , 1946, Mathematical Proceedings of the Cambridge Philosophical Society.

[4] Curtis T. McMullen,et al. The Hausdorff dimension of general Sierpiński carpets , 1984, Nagoya Mathematical Journal.

[5] K. Simon. Ergodic Theory of ℤ d Actions: Overlapping cylinders: the size of a dynamically defined Cantor-set , 1996 .

[6] K. Simon,et al. The Hausdorff dimension of -expansions with deleted digits , 1995 .

[7] H. Weiss,et al. On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle Conjecture , 1996 .

[8] Kenneth Falconer,et al. The Hausdorff dimension of some fractals and attractors of overlapping construction , 1987 .

[9] H. Weiss,et al. On the dimension of deterministic and random Cantor-like sets , 1994 .