ON RIGOROUS MATHEMATICAL DEFINITIONS OF CORRELATION DIMENSION AND GENERALIZED SPECTRUM FOR DIMENSIONS

被引：74

作者：

PESIN, YB

机构：

[1] Department of Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania

来源：

JOURNAL OF STATISTICAL PHYSICS | 1993年 / 71卷 / 3-4期

关键词：

DIMENSION; CORRELATION DIMENSION; HAUSDORFF DIMENSION; BOX DIMENSION; GENERALIZED SPECTRUM OF DIMENSIONS;

D O I：

10.1007/BF01058436

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as Hausdorff dimension, box dimension, etc. We also introduce different ways to define and study the generalized spectrum for dimensions-a one-parameter family of characteristics of dimension type.

引用

页码：529 / 547

页数：19

共 16 条

[1]

Billingsley P., 1965, ERGODIC THEORY INFOR

[2] CONNECTING ERGODICITY AND DIMENSION IN DYNAMIC-SYSTEMS [J].