A theoretical framework for the calculation of Hausdorff measure — Self-similar set satisfying OSC
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Abstract
A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established.
Key words
Haudorff measure open set conditionAMS (2010) subject classification
28A78 28A30 58F99Preview
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References
- [1]Falconer, K. J., The Geometry of Fractal Sets, Cambidge University Press.Google Scholar
- [2]Falconer, K. J., Fractal Geometry-Mathematical Foundations and Applications, John Wiley & Sons, Chichester New York Brisbane Toronto Singapore.Google Scholar
- [3]Falconer, K. J., Techniques in fractal geometry, John & Sons New York.Google Scholar
- [4]Marion, J., Measures de Hausdorff d’ensembles fractals, Ann. Sci. Math. Quebec, 11(1987), 111–32.MATHMathSciNetGoogle Scholar
- [5]Moran, M., Dynamical boundary of a self-similar set, Fundamenta Mathematicae, 160(1999), 1–14.MATHMathSciNetGoogle Scholar
- [6]Jia, B., Zhou, Z. and Zhu, Z., A Lower Bound for the Hausdorff Measure of the Sierpinski Gasket Nonlinearity, 15(2002), 393–404.MATHMathSciNetGoogle Scholar
- [7]Jia, B., Zhou, Z. and Zhu, Z., The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor set with Itself Acta Mathematica Sinica(in Chinese), 747–752.Google Scholar
- [8]Wang, X., On the Estimate and Conjecture of the Hausdorff Measure of the Sierpinski Gasket Progress in Natural Science(in Chinese), 9:6(1999), 488–493.Google Scholar
- [9]Walters, P., An Introduction to Ergodic Theory, (Berlin: Springer).Google Scholar
- [10]Zhou, Z., Hausdorff Measure of Koch Curve and Sierpinski Gasket, Progress in Natural Science, 7:4(1997), 401.MATHMathSciNetGoogle Scholar
- [11]Zhou, Z., Hausdorff Measure of Sierpinski Gasket, Science in China, Series A, 40:10(1997), 1016.CrossRefMATHMathSciNetGoogle Scholar
- [12]Zhou, Z., The Hausdorff Measures of the Self-similar Sets-the Koch Curve, Science in China, Series A, 41(1998), 723.CrossRefMATHGoogle Scholar
- [13]Zhou, Z., The Symbolic Dynamics, Shanghai Science and Education Press.Google Scholar
- [14]Zhou, Z. and Feng, L., Twelve Open Problems on the Exact Value of the Hausdorff Measure and on Topological Entropy: a Blief Survey of Recent Results, Nonlinearity, 17(2004), 493–502.CrossRefMATHMathSciNetGoogle Scholar
- [15]Zhou, Z. and Feng, L., A New Estimation of the Hausdorff Measure of the Sierpinski Gasket, Nonlinearity, 13(2000), 479–491.CrossRefMATHMathSciNetGoogle Scholar
- [16]Zhou, Z. and Feng, L., Twelve Open Problems on the Exact Value of the Hausdorff Measure and on Topological Entropy:a Brief Survey of Recent Results, Nonlinearity 17 (2004), 493–502.CrossRefMATHMathSciNetGoogle Scholar
- [17]Zhou, Z. and Wu, M., The Hausdorff Measure of a Sierpinski Carpet, Science in China, Series A, 47:7(1999), 673.MathSciNetGoogle Scholar
- [18]Zhou, Z., Wu, M. and Zhao, Y., The Hausdorff Measures of a Class of the Sierpinski Sponges, Chinese Annals of Mathematics(in Chinese) Series A, 22:1(2001), 57–64.MATHMathSciNetGoogle Scholar
- [19]Zhu, Z., Zhou, Z. and Jia, B., On the Lower Bound of the Hausdorff Measure of the Koch Curve, Acta Mathematica Sinica (in Chinese) 19:4(2003), 715–728.CrossRefMATHMathSciNetGoogle Scholar
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