Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian

1989 ◽  
Vol 56 (3-4) ◽  
pp. 525-531 ◽  
Author(s):  
András Sütő
Keyword(s):  
Continuous Spectrum ◽  
Lebesgue Measure ◽  
Cantor Set ◽  
Singular Continuous Spectrum

On the singular continuous spectrum of self-adjoint extensions

1996 ◽  
Vol 222 (4) ◽  
pp. 533-542 ◽  
Author(s):  
Johannes Brasche ◽  
Hagen Neidhardt
Keyword(s):  
Continuous Spectrum ◽  
Singular Continuous Spectrum

scholarly journals Duality and singular continuous spectrum in the almost Mathieu equation

1997 ◽  
Vol 178 (2) ◽  
pp. 169-183 ◽  
Author(s):  
A. Y. Gordon ◽  
S. Jitomirskaya ◽  
Y. Last ◽  
B. Simon
Keyword(s):  
Continuous Spectrum ◽  
Mathieu Equation ◽  
Singular Continuous Spectrum

Multifractal formalism for the inverse of random weak Gibbs measures

2019 ◽  
Vol 20 (04) ◽  
pp. 2050024
Author(s):  
Zhihui Yuan
Keyword(s):  
Probability Measure ◽  
Lebesgue Measure ◽  
Real Line ◽  
Gibbs Measures ◽  
Borel Probability Measure ◽  
Cantor Set ◽  
Multifractal Formalism ◽  
The Real ◽  
Random Dynamics ◽  
Borel Probability

Any Borel probability measure supported on a Cantor set included in [Formula: see text] and of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs measures. The study requires, in particular, to develop in this context of random dynamics a suitable version of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.

Linear measures of some sets of the Cantor type

1957 ◽  
Vol 53 (2) ◽  
pp. 312-317 ◽  
Author(s):  
Trevor J. Mcminn
Keyword(s):  
Lebesgue Measure ◽  
Measure Zero ◽  
Cartesian Product ◽  
Open Interval ◽  
Cantor Set ◽  
Unit Interval ◽  
Linear Measure ◽  
Closed Intervals ◽  
Image Position ◽  
Dense Set

1. Introduction. Let 0 < λ < 1 and remove from the closed unit interval the open interval of length λ concentric with the unit interval. From each of the two remaining closed intervals of length ½(1 − λ) remove the concentric open interval of length ½λ(1 − λ). From each of the four remaining closed intervals of length ¼λ(1 − λ)2 remove the concentric open interval of length ¼λ(l − λ)2, etc. The remaining set is a perfect non-dense set of Lebesgue measure zero and is the Cantor set for λ = ⅓. Let Tλr be the Cartesian product of this set with the set similar to it obtained by magnifying it by a factor r > 0. Letting L be Carathéodory linear measure (1) and letting G be Gillespie linear square(2), Randolph(3) has established the following relations:

On the singular continuous spectrum of self-adjoint extensions

1996 ◽  
Vol 222 (4) ◽  
pp. 533-542 ◽  
Author(s):  
Johannes Brasche ◽  
Hagen Neidhardt
Keyword(s):  
Continuous Spectrum ◽  
Singular Continuous Spectrum
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