Integrability of dynamical systems and the singular-point analysis

1985 ◽  
Vol 15 (6) ◽  
pp. 637-666 ◽  
Author(s):  
W. -H. Steeb ◽  
M. Kloke ◽  
B. M. Spieker ◽  
A. Kunick
Keyword(s):  
Dynamical Systems ◽  
Singular Point ◽  
Point Analysis

Hamiltonian systems with three degrees of freedom, singular-point analysis, and chaotic behavior

1986 ◽  
Vol 33 (3) ◽  
pp. 2131-2133 ◽  
Author(s):  
W.-H. Steeb ◽  
J. A. Louw ◽  
P. G. L. Leach ◽  
F. M. Mahomed
Keyword(s):  
Singular Point ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Chaotic Behavior ◽  
Point Analysis ◽  
Three Degrees Of Freedom

Singular point analysis, resonances and Yoshida's theorem

1987 ◽  
Vol 20 (12) ◽  
pp. 4027-4030 ◽  
Author(s):  
W -H Steeb ◽  
J A Louw ◽  
M F Maritz
Keyword(s):  
Singular Point ◽  
Point Analysis

Singular point analysis of the Gaudin equations

2008 ◽  
Vol 86 (6) ◽  
pp. 783-789 ◽  
Author(s):  
J R Schmidt
Keyword(s):  
Singular Point ◽  
Spin Model ◽  
Coupling Constants ◽  
Invariant Solutions ◽  
Painlevé Test ◽  
Rational Solutions ◽  
Systems Of Differential Equations ◽  
Point Analysis ◽  
All Solutions ◽  
Similarity Invariant

The Gaudin equations, a set of conditions of integrability imposed on the coupling constants of a lattice spin model, are solved by singular point analysis and the Painleve’ test. The Gaudin equations are transformed into systems of differential equations. The subset that are similarity-invariant have two, one, or zero constants of the motion corresponding to elliptic, trigonometric and (or) hyperbolic, and rational solutions, respectively. All solutions can be found at least formally by this technique. All similarity-invariant solutions are odd functions. There exist solutions with regular, even parts whose squares sum to a constant.PACS Nos.: 02.30.Ik, 02.40.Xx, 03.65.Fd

Energy eigenvalue levels and singular point analysis

1991 ◽  
Vol 152 (7) ◽  
pp. 339-342 ◽  
Author(s):  
W.-H. Steeb ◽  
W.D. Heiss
Keyword(s):  
Singular Point ◽  
Energy Eigenvalue ◽  
Point Analysis

Singular point analysis of nonlinear wave equations

1984 ◽  
Vol 39 (17) ◽  
pp. 429-432 ◽  
Author(s):  
W.-H. Steeb ◽  
M. Kloke ◽  
B. M. Spieker ◽  
A. Grauel
Keyword(s):  
Singular Point ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Point Analysis
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