Topological Pressure and Fractal Dimensions of Cookie-Cutter-Like Sets

Authors

Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2020

Abstract

The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero h of the pressure function. Moreover, it is shown that the h-dimensional Hausdorff measure and the h-dimensional packing measure are finite and positive.

Comments

Original published version available at https://www.seams-bull-math.ynu.edu.cn/downloadfile.jsp?filemenu=_202005&filename=10_44(5).pdf

Recommended Citation

Roychowdhury, Mrinal. 2020. “Topological Pressure and Fractal Dimensions of Cookie-Cutter-Like Sets.” Southeast Asian Bulletin of Mathematics 44 (5): 719–32. https://scholarworks.utrgv.edu/mss_fac/169

Publication Title

Southeast Asian Bulletin of Mathematics