Computer assisted proof of chaos in the Lorenz equations

被引：72

作者：

Galias, Z

Zgliczynski, P

机构：

[1] Stanislaw Staszic Univ Min & Met, Dept Elect Engn, PL-30059 Krakow, Poland

[2] Jagiellonian Univ, Math Inst, PL-30059 Krakow, Poland

来源：

PHYSICA D | 1998年 / 115卷 / 3-4期

关键词：

chaos; computer assisted proof;

D O I：

10.1016/S0167-2789(97)00233-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove with computer assistance the existence of chaos in a suitable Poincare map generated by the Lorenz system of equations. By chaos we mean the existence of symbolic dynamics with infinite number of periodic trajectories. The proof combines abstract results based on the fixed point index and finite rigorous computer calculations. Discussion concerning numerical algorithms is also included. Copyright (C) 1998 Elsevier Science B.V.

引用

页码：165 / 188

页数：24

共 33 条

[1]

AFRAIMOVICH VS, 1977, DOKL AKAD NAUK SSSR+, V234, P336

[2]

AFRAIMOVICH VS, 1983, T MOSCOW MATH SOC, V2, P153

[3]

[Anonymous], TOPOL METHODS NONLIN

[4]

Chen X., 1995, Lorenz equations, part iii: Existence of hyperbolic sets

[5]

CONLEY C, 1978, CBMS REGIONAL C SE M, V38

[6] ISOLATING BLOCKS AND EPSILON CHAINS FOR MAPS [J].

EASTON, R .

PHYSICA D, 1989, 39 (01) :95-110

[7] ISOLATING BLOCKS AND SYMBOLIC DYNAMICS [J].

EASTON, RW .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1975, 17 (01) :96-118

[8] Positive topological entropy of Chua's circuit: A computer assisted proof [J].

Galias, Z .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (02) :331-349

[9]

GREENBERG MJ, 1973, LECT ALGEBRAIC TOPOL

[10]

Guckenheimer J., 2013, Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields, DOI DOI 10.1007/978-1-4612-1140-2

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