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Journal of Fractal Geometry最新文献

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Geodesic interpolation on Sierpiński gaskets Sierpiński垫片上的测地线插值
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-12-13 DOI: 10.4171/JFG/100
Caitlin M. Davis, Laura A. LeGare, Cory McCartan, Luke G. Rogers
{"title":"Geodesic interpolation on Sierpiński gaskets","authors":"Caitlin M. Davis, Laura A. LeGare, Cory McCartan, Luke G. Rogers","doi":"10.4171/JFG/100","DOIUrl":"https://doi.org/10.4171/JFG/100","url":null,"abstract":"We study the analogue of a convex interpolant of two sets on Sierpinski gaskets and an associated notion of measure transport. The structure of a natural family of interpolating measures is described and an interpolation inequality is established. A key tool is a good description of geodesics on these gaskets, some results on which have previously appeared in the literature.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48766529","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: 2
A combinatorial Fredholm module on self-similar sets built on $n$-cubes 基于$n$-立方体的自相似集上的组合Fredholm模
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-12-12 DOI: 10.4171/jfg/132
T. Maruyama, Tatsuki Seto
{"title":"A combinatorial Fredholm module on self-similar sets built on $n$-cubes","authors":"T. Maruyama, Tatsuki Seto","doi":"10.4171/jfg/132","DOIUrl":"https://doi.org/10.4171/jfg/132","url":null,"abstract":"We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the Fredholm module.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44182743","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: 1
A characterization of metric subspaces of full Assouad dimension 全Assouad维度量子空间的一个刻画
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-11-25 DOI: 10.4171/jfg/109
Yoshito Ishiki
{"title":"A characterization of metric subspaces of full Assouad dimension","authors":"Yoshito Ishiki","doi":"10.4171/jfg/109","DOIUrl":"https://doi.org/10.4171/jfg/109","url":null,"abstract":"We introduce the notion of tiling spaces for metric space. The class of tiling spaces includes the Euclidean spaces, the middle-third Cantor spaces, and various self-similar spaces appeared in fractal geometry. On a tiling space, we characterize a metric subspace whose Assouad dimension coincides with that of the whole space.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47854872","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: 1
On the dimension spectra of infinite conformal iterated function systems 无穷保角迭代函数系统的维谱
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-10-22 DOI: 10.4171/JFG/112
Tushar Das, David Simmons
{"title":"On the dimension spectra of infinite conformal iterated function systems","authors":"Tushar Das, David Simmons","doi":"10.4171/JFG/112","DOIUrl":"https://doi.org/10.4171/JFG/112","url":null,"abstract":"The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43077824","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: 1
Projection theorems for intermediate dimensions 中间维的投影定理
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-07-17 DOI: 10.4171/JFG/99
Stuart A. Burrell, K. Falconer, J. Fraser
{"title":"Projection theorems for intermediate dimensions","authors":"Stuart A. Burrell, K. Falconer, J. Fraser","doi":"10.4171/JFG/99","DOIUrl":"https://doi.org/10.4171/JFG/99","url":null,"abstract":"Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain kernels. Then, relying on this, we show that the intermediate dimensions of the projection of a set $E subset R^n$ onto almost all $m$-dimensional subspaces depend only on $m$ and $E$, that is, they are almost surely independent of the choice of subspace. Our approach is based on `intermediate dimension profiles' which are expressed in terms of capacities.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41628992","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: 17
Eigenvalue bounds and spectral asymptotics for fractal Laplacians 分形拉普拉斯算子的特征值界和谱渐近性
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-03-21 DOI: 10.4171/JFG/71
J. P. Pinasco, Cristian Scarola
{"title":"Eigenvalue bounds and spectral asymptotics for fractal Laplacians","authors":"J. P. Pinasco, Cristian Scarola","doi":"10.4171/JFG/71","DOIUrl":"https://doi.org/10.4171/JFG/71","url":null,"abstract":"","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/71","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42736505","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
Geometry and Laplacian on discrete magic carpets 离散魔毯上的几何和拉普拉斯
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-02-09 DOI: 10.4171/jfg/129
E. Goodman, Chunyin Siu, R. Strichartz
{"title":"Geometry and Laplacian on discrete magic carpets","authors":"E. Goodman, Chunyin Siu, R. Strichartz","doi":"10.4171/jfg/129","DOIUrl":"https://doi.org/10.4171/jfg/129","url":null,"abstract":"We study several variants of the classical Sierpinski Carpet (SC) fractal. The main examples we call infinite magic carpets (IMC), obtained by taking an infinite blowup of a discrete graph approximation to SC and identifying edges using torus, Klein bottle or projective plane type identifications. We use both theoretical and experimental methods. We prove estimates for the size of metric balls that are close to optimal. We obtain numerical approximations to the spectrum of the graph Laplacian on IMC and to solutions of the associated differential equations: Laplace equation, heat equation and wave equation. We present evidence that the random walk on IMC is transient, and that the full spectral resolution of the Laplacian on IMC involves only continuous spectrum. This paper is a contribution to a general program of eliminating unwanted boundaries in the theory of analysis on fractals.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45363982","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: 0
Construction and box dimension of recurrent fractal interpolation surfaces 循环分形插值曲面的构造与盒维数
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-02-04 DOI: 10.4171/JFG/105
Zhen Liang, H. Ruan
{"title":"Construction and box dimension of recurrent fractal interpolation surfaces","authors":"Zhen Liang, H. Ruan","doi":"10.4171/JFG/105","DOIUrl":"https://doi.org/10.4171/JFG/105","url":null,"abstract":"In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy to be generated while there are no restrictions on interpolation points and vertical scaling factors. We also obtain the box dimension of bilinear RFISs under certain constraints, where the main assumption is that vertical scaling factors have uniform sums under a compatible partition.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45744205","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: 9
Assouad type dimensions for self-affine sponges with a weak coordinate ordering condition 具有弱坐标有序条件的自仿射海绵的种类尺寸
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-02-01 DOI: 10.4171/JFG/69
D. Howroyd
{"title":"Assouad type dimensions for self-affine sponges with a weak coordinate ordering condition","authors":"D. Howroyd","doi":"10.4171/JFG/69","DOIUrl":"https://doi.org/10.4171/JFG/69","url":null,"abstract":"","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/69","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70871739","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: 0
Rational families converging to a family of exponential maps 收敛于指数映射族的有理族
IF 0.8 4区 数学
Journal of Fractal Geometry Pub Date : 2019-02-01 DOI: 10.4171/JFG/70
Joanna Furno, J. Hawkins, L. Koss
{"title":"Rational families converging to a family of exponential maps","authors":"Joanna Furno, J. Hawkins, L. Koss","doi":"10.4171/JFG/70","DOIUrl":"https://doi.org/10.4171/JFG/70","url":null,"abstract":"We analyze the dynamics of a sequence of families of non-polynomial rational maps, tfa,du, for a P C ̊ “ Czt0u, d ě 2. For each d, tfa,du is a family of rational maps of degree d of the Riemann sphere parametrized by a P C ̊. For each a P C ̊, as d Ñ 8, fa,d converges uniformly on compact sets to a map fa that is conformally conjugate to a transcendental entire map on C. We study how properties of the families fa,d contribute to our understanding of the dynamical properties of the limiting family of maps. We show all families have a common connectivity locus; moreover the rational maps contain some well-studied examples. Mathematics Subject Classification (2010). 37F10, 37F45, 30D05.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/70","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44935513","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
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