Journal of Fractal Geometry最新文献_第5页

A capacity approach to box and packing dimensions of projections of sets and exceptional directions 集和例外方向的投影的盒和包装尺寸的容量方法

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2019-01-30 DOI: 10.4171/jfg/96

K. Falconer

引用次数: 14

Polynomials on the Sierpiński gasket with respect to different Laplacians which are symmetric and self-similar 关于不同拉普拉斯算子的Sierpiński垫圈上的多项式是对称的和自相似的

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2019-01-25 DOI: 10.4171/jfg/95

C. Loring, W. J. Ogden, Ely Sandine, R. Strichartz

引用次数: 4

Connectedness of attractors of a certain family of IFSs 一类ifs族吸引子的连通性

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-12-16 DOI: 10.4171/jfg/89

F. Strobin, J. Swaczyna

引用次数: 2

Absolute continuity in families of parametrised non-homogeneous self-similar measures 参数化非齐次自相似测度族中的绝对连续性

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-12-12 DOI: 10.4171/jfg/127

A. Käenmäki, Tuomas Orponen

引用次数: 5

Improved bounds for the dimensions of planar distance sets 平面距离集维数的改进边界

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-11-08 DOI: 10.4171/jfg/97

Pablo Shmerkin

引用次数: 18

Global fractal transformations and global addressing 全局分形变换与全局寻址

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-07-27 DOI: 10.4171/JFG/65

A. Vince

引用次数: 2

Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators 准周期Schrödinger算子Hölder连续性的频率依赖性

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-07-26 DOI: 10.4171/JFG/68

P. Munger

引用次数: 4

Quasi-doubling of self-similar measures with overlaps 具有重叠的自相似测度的拟加倍

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-07-24 DOI: 10.4171/jfg/91

K. Hare, K. Hare, Sascha Troscheit

{"title":"Quasi-doubling of self-similar measures with overlaps","authors":"K. Hare, K. Hare, Sascha Troscheit","doi":"10.4171/jfg/91","DOIUrl":"https://doi.org/10.4171/jfg/91","url":null,"abstract":"The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity dimension. One reason for the interest in this notion is that a measure has finite Assouad dimension if and only if it is doubling. \u0000Motivated by recent progress on both the Assouad dimension of measures that satisfy a strong separation condition and the quasi-Assouad dimension of metric spaces, we introduce the notion of the quasi-Assouad dimension of a measure. As with sets, the quasi-Assouad dimension of a measure is dominated by its Assouad dimension. It dominates both the quasi-Assouad dimension of its support and the supremal local dimension of the measure, with strict inequalities possible in all cases. \u0000Our main focus is on self-similar measures in $mathbb{R}$ whose support is an interval and which may have `overlaps'. For measures that satisfy a weaker condition than the weak separation condition we prove that finite quasi-Assouad dimension is equivalent to quasi-doubling of the measure, a strictly less restrictive property than doubling. Further, we exhibit a large class of such measures for which the quasi-Assouad dimension coincides with the maximum of the local dimension at the endpoints of the support. This class includes all regular, equicontractive self-similar measures satisfying the weak separation condition, such as convolutions of uniform Cantor measures with integer ratio of dissection. Other properties of this dimension are also established and many examples are given.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44969257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Embedding fractals in Banach, Hilbert or Euclidean spaces 在巴拿赫、希尔伯特或欧几里得空间中嵌入分形

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-06-21 DOI: 10.4171/JFG/94

T. Banakh, M. Nowak, F. Strobin

{"title":"Embedding fractals in Banach, Hilbert or Euclidean spaces","authors":"T. Banakh, M. Nowak, F. Strobin","doi":"10.4171/JFG/94","DOIUrl":"https://doi.org/10.4171/JFG/94","url":null,"abstract":"By a metric fractal we understand a compact metric space $K$ endowed with a finite family $mathcal F$ of contracting self-maps of $K$ such that $K=bigcup_{finmathcal F}f(K)$. If $K$ is a subset of a metric space $X$ and each $finmathcal F$ extends to a contracting self-map of $X$, then we say that $(K,mathcal F)$ is a fractal in $X$. We prove that each metric fractal $(K,mathcal F)$ is \u0000$bullet$ isometrically equivalent to a fractal in the Banach spaces $C[0,1]$ and $ell_infty$; \u0000$bullet$ bi-Lipschitz equivalent to a fractal in the Banach space $c_0$; \u0000$bullet$ isometrically equivalent to a fractal in the Hilbert space $ell_2$ if $K$ is an ultrametric space. \u0000We prove that for a metric fractal $(K,mathcal F)$ with the doubling property there exists $kinmathbb N$ such that the metric fractal $(K,mathcal F^{circ k})$ endowed with the fractal structure $mathcal F^{circ k}={f_1circdotscirc f_k:f_1,dots,f_kinmathcal F}$ is equi-H\"older equivalent to a fractal in a Euclidean space $mathbb R^d$. This result is used to prove our main result saying that each finite-dimensional compact metrizable space $K$ containing an open uncountable zero-dimensional space $Z$ is homeomorphic to a fractal in a Euclidean space $mathbb R^d$. For $Z$, being a copy of the Cantor set, this embedding result was proved by Duvall and Husch in 1992.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43637647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Modeling the fractal geometry of Arctic melt ponds using the level sets of random surfaces 利用随机曲面的水平集对北极融池的分形几何建模

IF 0.8 4区数学

Journal of Fractal Geometry Pub Date : 2018-06-04 DOI: 10.4171/JFG/58

B. Bowen, C. Strong, K. Golden

{"title":"Modeling the fractal geometry of Arctic melt ponds using the level sets of random surfaces","authors":"B. Bowen, C. Strong, K. Golden","doi":"10.4171/JFG/58","DOIUrl":"https://doi.org/10.4171/JFG/58","url":null,"abstract":"During the late spring, most of the Arctic Ocean is covered by sea ice with a layer of snow on top. As the snow and sea ice begin to melt, water collects on the surface to form melt ponds. As melting progresses, sparse, disconnected ponds coalesce to form complex, self-similar structures which are connected over large length scales. The boundaries of the ponds undergo a transition in fractal dimension from 1 to about 2 around a critical length scale of 100 square meters, as found previously from area–perimeter data. Melt pond geometry depends strongly on sea ice and snow topography. Here we construct a rather simple model of melt pond boundaries as the intersection of a horizontal plane, representing the water level, with a random surface representing the topography. We show that an autoregressive class of anisotropic random Fourier surfaces provides topographies that yield the observed fractal dimension transition, with the ponds evolving and growing as the plane rises. The results are compared with a partial differential equation model of melt pond evolution that includes much of the physics of the system. Properties of the shift in fractal dimension, such as its amplitude, phase and rate, are shown to depend on the surface anisotropy and autocorrelation length scales in the models. Melting-driven differences between the two models are highlighted. Mathematics Subject Classification (2010). 51, 35, 42, 86.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/58","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45646360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12