On the Hausdorff dimension of rademacher Riesz products

1990 ◽  
Vol 110 (1) ◽  
pp. 15-21 ◽  
Author(s):  
A. Bisbas ◽  
C. Karanikas
Keyword(s):  
Hausdorff Dimension ◽  
Riesz Products

Riesz products, Hausdorff dimension and normal numbers

1987 ◽  
Vol 101 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Gavin Brown ◽  
William Moran ◽  
Charles E. M. Pearce
Keyword(s):  
Hausdorff Dimension ◽  
Real Number ◽  
Normal Numbers ◽  
Riesz Products

We say a real number x is normal to base r if the sequence is uniformly distributed modulo [0, 1]. Pollington[10] has proved the following result concerning the normality of numbers.

THE HAUSDORFF DIMENSION OF VERY STRONGLY POROUS SETS IN R n

1987 ◽  
Vol 13 (1) ◽  
pp. 33
Author(s):  
Mattila
Keyword(s):  
Hausdorff Dimension ◽  
Porous Sets

Infinite Graph-Directed Systems and Hausdorff Dimension

2017 ◽  
Vol 3 (1) ◽  
pp. 84-95
Author(s):  
Amit Priyadarshi
Keyword(s):  
Hausdorff Dimension ◽  
Infinite Graph

scholarly journals Minimal F2-flows

1985 ◽  
Vol 39 (2) ◽  
pp. 187-193
Author(s):  
Daniel Berend
Keyword(s):  
Hausdorff Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Affine Transformations ◽  
Dimensional Torus ◽  
Minimal Sets ◽  
Necessary And Sufficient

AbstractLet σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.

Length distortion and the Hausdorff dimension of limit sets

2000 ◽  
Vol 122 (3) ◽  
pp. 465-482 ◽  
Author(s):  
Martin Bridgeman ◽  
Edward C. Taylor
Keyword(s):  
Hausdorff Dimension ◽  
Limit Sets ◽  
Length Distortion

scholarly journals A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1546
Author(s):  
Mohsen Soltanifar
Keyword(s):  
Hausdorff Dimension ◽  
Lebesgue Measure ◽  
Virtual World ◽  
Fractal Dimensions ◽  
Definition Of ◽  
The Given

How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure. We prove the existence of aleph-two of virtual fractals with a Hausdorff dimension of a bi-variate function of them and the given Lebesgue measure. The question remains unanswered for other fractal dimensions.

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