CALCULATING STABLE AND UNSTABLE MANIFOLDS

被引:69
作者
You, Zhiping [1 ]
Kostelich, Eric J. [2 ,3 ]
Yorke, James A. [1 ,3 ]
机构
[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA
[2] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA
[3] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1991年 / 1卷 / 03期
关键词
D O I
10.1142/S0218127491000440
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A numerical procedure is described for computing the successive images of a curve under a diffeomorphism of R-N. Given a tolerance epsilon, we show how to rigorously guarantee that each point on the computed curve lies no further than a distance e from the "true" image curve. In particular, if e is the distance between adjacent points (pixels) on a computer screen, then a plot of the computed curve coincides with the true curve within the resolution of the display. A second procedure is described to minimize the amount of computation of parts of the curve that lie outside a region of interest. We apply the method to compute the one-dimensional stable and unstable manifolds of the Henon and Ikeda maps, as well as a Poincare map for the forced damped pendulum.
引用
收藏
页码:605 / 623
页数:19
相关论文
共 18 条
[1]  
BARGE M, 1987, P AM MATH SOC, V101, P541
[2]  
Devaney R L, 1989, INTRO CHAOTIC DYNAMI
[3]   STABLE AND UNSTABLE MANIFOLDS OF THE HENON MAPPING [J].
FRANCESCHINI, V ;
RUSSO, L .
JOURNAL OF STATISTICAL PHYSICS, 1981, 25 (04) :757-769
[4]   BASIN BOUNDARY METAMORPHOSES - CHANGES IN ACCESSIBLE BOUNDARY ORBITS [J].
GREBOGI, C ;
OTT, E ;
YORKE, JA .
PHYSICA D, 1987, 24 (1-3) :243-262
[5]   MULTI-DIMENSIONED INTERTWINED BASIN BOUNDARIES - BASIN STRUCTURE OF THE KICKED DOUBLE ROTOR [J].
GREBOGI, C ;
KOSTELICH, E ;
OTT, E ;
YORKE, JA .
PHYSICA D, 1987, 25 (1-3) :347-360
[6]   CRISES, SUDDEN CHANGES IN CHAOTIC ATTRACTORS, AND TRANSIENT CHAOS [J].
GREBOGI, C ;
OTT, E ;
YORKE, JA .
PHYSICA D, 1983, 7 (1-3) :181-200
[7]  
Guckenheimer J., 2013, APPL MATH SCI, DOI 10.1007/978-1-4612- 1140-2
[8]   GLOBAL DYNAMICAL BEHAVIOR OF THE OPTICAL-FIELD IN A RING CAVITY [J].
HAMMEL, SM ;
JONES, CKRT ;
MOLONEY, JV .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 1985, 2 (04) :552-564
[9]   2-DIMENSIONAL MAPPING WITH A STRANGE ATTRACTOR [J].
HENON, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1976, 50 (01) :69-77
[10]   MULTIPLE-VALUED STATIONARY STATE AND ITS INSTABILITY OF THE TRANSMITTED LIGHT BY A RING CAVITY SYSTEM [J].
IKEDA, K .
OPTICS COMMUNICATIONS, 1979, 30 (02) :257-261