Stable Intersections of Regular Cantor Sets with Large Hausdorff Dimensions

2001 ◽  
Vol 154 (1) ◽  
pp. 45 ◽  
Author(s):  
Carlos Gustavo T. de A. Moreira ◽  
Jean-Christophe Yoccoz
Keyword(s):  
Cantor Sets ◽  
Hausdorff Dimensions

Corrigendum Stable Intersections of Regular Cantor Sets with Large Hausdorff Dimensions

2001 ◽  
Vol 154 (2) ◽  
pp. 527 ◽  
Author(s):  
Carlos Gustavo T. de A. Moreira ◽  
Jean-Christophe Yoccoz
Keyword(s):  
Cantor Sets ◽  
Hausdorff Dimensions

scholarly journals Assouad Dimensions and Lower Dimensions of Some Moran Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
JiaQing Xiao
Keyword(s):  
Compression Ratio ◽  
Cantor Sets ◽  
Hausdorff Dimensions ◽  
Low Dimensions ◽  
Assouad Dimension ◽  
Packing Dimensions ◽  
Box Dimensions

We prove that the low dimensions of a class of Moran sets coincide with their Hausdorff dimensions and obtain a formula for the lower dimensions. Subsequently, we consider some homogeneous Cantor sets which belong to Moran sets and give the counterexamples in which their Assouad dimension is not equal to their upper box dimensions and packing dimensions under the case of not satisfying the condition of the smallest compression ratio c ∗ > 0 .

Symmetric Porosity and Symmetric Cantor Sets

1991 ◽  
Vol 17 (1) ◽  
pp. 19
Author(s):  
Evans
Keyword(s):  
Cantor Sets

scholarly journals On the Spectra of Separable 2D Almost Mathieu Operators

2021 ◽  
Author(s):  
Alberto Takase
Keyword(s):  
Positive Measure ◽  
Schrödinger Operators ◽  
Cantor Sets ◽  
Schrodinger Operators ◽  
Discrete Schrödinger Operators ◽  
Mathieu Operator ◽  
Almost Mathieu Operator

AbstractWe consider separable 2D discrete Schrödinger operators generated by 1D almost Mathieu operators. For fixed Diophantine frequencies, we prove that for sufficiently small couplings the spectrum must be an interval. This complements a result by J. Bourgain establishing that for fixed couplings the spectrum has gaps for some (positive measure) Diophantine frequencies. Our result generalizes to separable multidimensional discrete Schrödinger operators generated by 1D quasiperiodic operators whose potential is analytic and whose frequency is Diophantine. The proof is based on the study of the thickness of the spectrum of the almost Mathieu operator and utilizes the Newhouse Gap Lemma on sums of Cantor sets.

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