A DYNAMIC SYSTEM WITH INTEGER INFORMATION DIMENSION AND FRACTAL CORRELATION EXPONENT

被引：4

作者：

CUTLER, CD

机构：

[1] Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1, Ontario

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1990年 / 129卷 / 03期

关键词：

D O I：

10.1007/BF02097108

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we construct a family {Tγ}, 0<γ<1/2, of exact endomorphisms of [0, 1] such that the invariant measure mγ of Tγ is equivalent to Lebesgue measure but has fractal correlation exponent ν=2γ. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems. © 1990 Springer-Verlag.

引用

页码：621 / 629

页数：9

共 11 条

[1]

Collet P., 1983, ERGOD THEOR DYN SYST, V3, P13

[2]

CUTLER CD, 1989, SOME RESULTS BEHAVIO

[3] THE DIMENSION OF CHAOTIC ATTRACTORS [J].