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Selfsimilar measures for quasicrystals
 CRM Monograph Series, vol. 13, AMS, Rhode Island (2000
"... Abstract. We study selfsimilar measures of Hutchinson type, defined by compact families of contractions, both in a single and multicomponent setting. The results are applied in the context of general model sets to infer, via a generalized version of Weyl’s Theorem on uniform distribution, the exis ..."
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Cited by 14 (7 self)
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Abstract. We study selfsimilar measures of Hutchinson type, defined by compact families of contractions, both in a single and multicomponent setting. The results are applied in the context of general model sets to infer, via a generalized version of Weyl’s Theorem on uniform distribution
SelfSimilar Measures
"... . After an introduction to selfsimilar deterministic and random measures, we introduce an algorithm which decides on the separation condition for given similarity mappings dening a selfsimilar set. We construct some new types of Sierpinski gasket and determine their exponent of interior distance. ..."
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Cited by 1 (0 self)
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. After an introduction to selfsimilar deterministic and random measures, we introduce an algorithm which decides on the separation condition for given similarity mappings dening a selfsimilar set. We construct some new types of Sierpinski gasket and determine their exponent of interior distance
MOMENT MATRIX OF SELFSIMILAR MEASURES
"... Abstract. We give in this paper an expression for the moment matrix associated to a selfsimilar measure given by an Iterated Function Systems (IFS). This expression translates the selfsimilarity property of a measure to its moment matrix. This matrix relation shows that the properties of a measure ..."
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Abstract. We give in this paper an expression for the moment matrix associated to a selfsimilar measure given by an Iterated Function Systems (IFS). This expression translates the selfsimilarity property of a measure to its moment matrix. This matrix relation shows that the properties of a
Densities of SelfSimilar Measures on the Line
, 1995
"... this article are presented in schematic form. Of course, they were actually coded in computer programs: see the section on Electronic Availability at the end. The programs were written in C and Pascal and run on a Sun Sparcstation using Unix during the summer of 1993. This article contains some conv ..."
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Cited by 3 (0 self)
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. In particular, the material in Sections 4 and 5 is almost entirely serendipitous discovery in response to the experimental results. The reader is encouraged to consult [Barnsley 1988] and [Falconer 1990] for the general theory of iterated function systems and selfsimilar measures. 104 Experimental Mathematics
Multifractality of overlapping nonuniform selfsimilar measures
"... We prove that nonuniform selfsimilar measures have a multifractal spectrum in a parameter domain where the open set condition fails to hold. MSC 2010: 28A80 Keywords: selfsimilar measures, multifractal analysis, dimension spectrum, local dimension, potential theory, transversality 1 ..."
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We prove that nonuniform selfsimilar measures have a multifractal spectrum in a parameter domain where the open set condition fails to hold. MSC 2010: 28A80 Keywords: selfsimilar measures, multifractal analysis, dimension spectrum, local dimension, potential theory, transversality 1
THE PARAMETER DISTRIBUTION SET FOR A SELFSIMILAR MEASURE
"... Abstract. The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a selfsimilar measure on a selfsimilar set satisfying the open set condition. 1. ..."
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Abstract. The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a selfsimilar measure on a selfsimilar set satisfying the open set condition. 1.
The Absolute Continuity of a Family of SelfSimilar Measures
, 2008
"... Abstract. For a class of selfsimilar measures defined by iterated function system on the line with equal equal probability weights, the absolute continuity has been proved by using a technique of polynomial. This extends a result of Garsia on infinite Bernulli convolution. Also, this result provid ..."
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Abstract. For a class of selfsimilar measures defined by iterated function system on the line with equal equal probability weights, the absolute continuity has been proved by using a technique of polynomial. This extends a result of Garsia on infinite Bernulli convolution. Also, this result
RENEWAL OF SINGULARITY SETS OF RANDOM SELFSIMILAR MEASURES
 APPLIED PROBABILITY TRUST (9 FEBRUARY 2007)
, 2007
"... This paper investigates new properties concerning the multifractal structure of a class of random selfsimilar measures. These measures include the wellknown Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure o ..."
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Cited by 4 (2 self)
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This paper investigates new properties concerning the multifractal structure of a class of random selfsimilar measures. These measures include the wellknown Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure
Results 1  10
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1,311,671