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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F14%3A10286403%21RIV15-MSM-11320___
rdf:type
skos:Concept n17:Vysledek
dcterms:description
Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents. Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents.
dcterms:title
Scaling exponents of curvature measures Scaling exponents of curvature measures
skos:prefLabel
Scaling exponents of curvature measures Scaling exponents of curvature measures
skos:notation
RIV/00216208:11320/14:10286403!RIV15-MSM-11320___
n3:aktivita
n7:P n7:I
n3:aktivity
I, P(GCP201/10/J039)
n3:cisloPeriodika
2
n3:dodaniDat
n6:2015
n3:domaciTvurceVysledku
n18:5312493
n3:druhVysledku
n9:J
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
43853
n3:idVysledku
RIV/00216208:11320/14:10286403
n3:jazykVysledku
n12:eng
n3:klicovaSlova
locally flat; self-similar set; scaling exponent; fractal curvature; S-dimension; Minkowski dimension; curvature-direction measure; curvature measure; Parallel set
n3:klicoveSlovo
n8:fractal%20curvature n8:scaling%20exponent n8:self-similar%20set n8:Minkowski%20dimension n8:locally%20flat n8:Parallel%20set n8:curvature%20measure n8:curvature-direction%20measure n8:S-dimension
n3:kodStatuVydavatele
CH - Švýcarská konfederace
n3:kontrolniKodProRIV
[7633472C0075]
n3:nazevZdroje
Journal of fractal geometry
n3:obor
n4:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:GCP201%2F10%2FJ039
n3:rokUplatneniVysledku
n6:2014
n3:svazekPeriodika
2014/1
n3:tvurceVysledku
Winter, Steffen Pokorný, Dušan
s:issn
2308-1309
s:numberOfPages
43
n14:doi
10.4171/JFG/5
n13:organizacniJednotka
11320