Spectral triples for nested fractals

被引：5

作者：

Guido, Daniele ^{[1
]}

Isola, Tommaso ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2017年 / 11卷 / 04期

关键词：

Spectral triple; nested fractal; self-similar energy; Hausdorff dimension; noncommutative distance; SELF-SIMILAR FRACTALS; DIRICHLET FORMS; SIERPINSKI GASKET; DIRAC OPERATORS; DIXMIER TRACES; SETS; LAPLACIANS; GEOMETRY; CONVERGENCE; DIFFUSIONS;

D O I：

10.4171/JNCG/11-4-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that, for nested fractals [31], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (when it exists) induced by the immersion in R-n, and the self-similar energy can all be recovered by the description of the fractals in terms of the spectral triples considered in [18].

引用

页码：1413 / 1436

页数：24

共 37 条

[1]

Barlow M., 1998, Lecture Notes in Math., V1690, P1, DOI [10.1007/BFb0092537, DOI 10.1007/BFB0092537]

[2]

Bondy J. A., 1976, Graph Theory with Applications

[3] Electrical resistance of N-gasket fractal networks [J].

Boyle, Brighid ;

Cekala, Kristin ;

Ferrone, David ;

Rifkin, Neil ;

Teplyaev, Alexander .

PACIFIC JOURNAL OF MATHEMATICS, 2007, 233 (01) :15-40

[4]

BUYALO S.V., 2000, ALGEBRA ANALIZ, V12, P1

[5] Spectral flow and Dixmier traces [J].

Carey, A ;

Phillips, J ;

Sukochev, F .

ADVANCES IN MATHEMATICS, 2003, 173 (01) :68-113

[6] Dirac operators and spectral triples for some fractal sets built on curves [J].

Christensen, Erik ;

Ivan, Cristina ;

Lapidus, Michel L. .

ADVANCES IN MATHEMATICS, 2008, 217 (01) :42-78

[7]

Christensen E, 2007, MATH SCAND, V100, P35

[8] Spectral triples and the geometry of fractals [J].

Christensen, Erik ;

Ivan, Cristina ;

Schrohe, Elmar .

JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2012, 6 (02) :249-274

[9] Derivations as square roots of Dirichlet forms [J].

Cipriani, F ;

Sauvageot, JL .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 201 (01) :78-120

[10] Spectral triples for the Sierpinski gasket [J].

Cipriani, Fabio ;

Guido, Daniele ;

Isola, Tommaso ;

Sauvageot, Jean-Luc .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (08) :4809-4869

← 1 2 3 4 →