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

[11] EFFICIENT COMPUTATION OF COMPLEX ERROR FUNCTION [J].

GAUTSCHI, W .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1970, 7 (01) :187-&

[12] CHARACTERIZATION OF STRANGE ATTRACTORS [J].

GRASSBERGER, P ;

PROCACCIA, I .

PHYSICAL REVIEW LETTERS, 1983, 50 (05) :346-349

[13]

Guckenheimer J., 2013, APPL MATH SCI, DOI 10.1007/978-1-4612- 1140-2

[14]

HENRICI P, 1977, APPLIED COMPUTATIONA, V2

[15] FRUSTRATED INSTABILITIES IN NONLINEAR OPTICAL RESONATORS [J].

IKEDA, K ;

MIZUNO, M .

PHYSICAL REVIEW LETTERS, 1984, 53 (14) :1340-1343

[16]

Jones William B., 1984, ENCY MATH ITS APPL, pi

[17]

Khinchin A., 1963, CONTINUED FRACTIONS

[18] PERIOD 3 IMPLIES CHAOS [J].

LI, TY ;

YORKE, JA .

AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (10) :985-992

[19]

Ma~n~e R., 1987, ERGODIC THEORY DIFFE

[20]

NIVEN I, 1956, MAA CARUS MATH MONOG, V11

← 1 2 3 4 →