On the construction, properties and Hausdorff dimension of random Cantor one <em>p</em>^<em>th</em> set

Abstract

In 1883, German Mathematician George Cantor introduced Cantor ternary set which is a self-similar fractal. K. J. Falconer (1990) defined random Cantor set with statistical self-similarity. The purpose of this paper is to introduce generalized random Cantor sets (one 5th, one 7th and in general one pth). Some properties and results of random Cantor one pth set have also been obtained. We compute Hausdorff dimension of random Cantor one pth sets and show that Hausdorff dimension of these random Cantor sets is less than that of Hausdorff dimension of Cantor one pth sets, calculated by Ashish et al. (2013).

Keywords

• nonlinear dynamics
• random construction
• random cantor one <i>p</i>^<i>th</i> set
• hausdorff dimension
• martingale
• probability