CHAOS AND CONTINUED FRACTIONS

被引：19

作者：

CORLESS, RM

FRANK, GW

MONROE, JG

机构：

[1] Department of Applied Mathematics, University of Western Ontario, London, Ont.

来源：

PHYSICA D | 1990年 / 46卷 / 02期

关键词：

D O I：

10.1016/0167-2789(90)90038-Q

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper reports the use of the Gauss map from the theory of simple continued fractions as an example of a chaotic discrete dynamical system. Because of the simplicity of the map and the wealth of classical mathematical results, we are able to gain insight into the interaction between exact dynamical systems and their floating-point simulations. We calculate the correlation dimension and the capacity dimension of the Gauss map, and use these to examine current reconstruction techniques. © 1990.

引用

页码：241 / 253

页数：13

共 31 条

[1]

[Anonymous], 1981, LECT NOTES MATH, V854, P454

[2]

Billingsley P., 1965, ERGODIC THEORY INFOR

[3]

BIRKHOFF GD, 1982, B SOC MATH FRANCE, V60, P1

[4]

BLOCK L, 1979, SPRINGER LECT NTOES, V819, P18

[5]

Borwein J. M., 1987, PI AGM STUDY ANAL NU

[6]

CHAR BW, 1988, MAPLE USERS MANUAL

[7]

Chillingworth D., 1976, DIFFERENTIAL TOPOLOG

[8] COMPUTER-DRAWN PICTURES STALK THE WILD TRAJECTORY [J].

CIPRA, BA .

SCIENCE, 1988, 241 (4870) :1162-1163

[9]

DEVANEY R, 1985, INTRO CHAOTIC DYNAMI

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

FARMER, JD ;

OTT, E ;

YORKE, JA .

PHYSICA D-NONLINEAR PHENOMENA, 1983, 7 (1-3) :153-180

← 1 2 3 4 →