On an embedding theorem

被引：14

作者：

Caballero, V ^{[1
]}

机构：

[1] Univ Murcia, Fac Econ & Empresa, Dept Metodos Cuantitat Econ, Murcia, Spain

来源：

ACTA MATHEMATICA HUNGARICA | 2000年 / 88卷 / 04期

关键词：

Time Series; Dynamical System; Embed Theorem;

D O I：

10.1023/A:1026753605784

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a theorem giving conditions under which a discrete-time dynamical system as (x(t), y(t)) = (f(x(t-1), y(t-1)), g(x(t-1), y(t-1))) can be reconstructed from a scalar valued time series (alpha(t))(t) which depends only on x(t) where alpha(t) = alpha(x(t)). This theorem allows us to use the delay-coordinate method in this setting.

引用

页码：269 / 278

页数：10

共 13 条

[1]

[Anonymous], TRANSVERSAL MAPPING

[2]

[Anonymous], 1994, COPING CHAOS

[3]

[Anonymous], 1993, Dimension estimation and models

[4] ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].

ECKMANN, JP ;

RUELLE, D .

REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656

[5]

FOSTER MJ, 1975, J LOND MATH SOC, V11, P65

[6]

Hirsch M. W., 1994, Differential Topology

[7] THE TAKENS EMBEDDING THEOREM [J].

Noakes, Lyle .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1991, 1 (04) :867-872

[8]

Robinson C., 1995, Dynamical systems: stability, symbolic dynamics, and chaos

[9] EMBEDOLOGY [J].

SAUER, T ;

YORKE, JA ;

CASDAGLI, M .

JOURNAL OF STATISTICAL PHYSICS, 1991, 65 (3-4) :579-616

[10] Takens embedding theorems for forced and stochastic systems [J].

Stark, J ;

Broomhead, DS ;

Davies, ME ;

Huke, J .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (08) :5303-5314

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