Solvable dynamical systems and isospectral matrices defined in terms of the zeros of orthogonal or otherwise special polynomials

2018 ◽  
pp. 122-158
Author(s):  
Norbert Euler
Keyword(s):  
Dynamical Systems ◽  
Special Polynomials ◽  
Solvable Dynamical Systems

Singularities in the complex time plane and exactly solvable dynamical systems

1994 ◽  
Vol 72 (3-4) ◽  
pp. 147-151 ◽  
Author(s):  
W.-H. Steeb ◽  
Assia Fatykhova
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Numerical Study ◽  
Complex Time ◽  
Nonlinear Dynamical ◽  
Singularity Structure ◽  
Exactly Solvable ◽  
Solvable Dynamical Systems

A powerful tool in the study of nonlinear dynamical systems is the investigation of the singularity structure in the complex time plane. In most cases the singularity structure can only be found numerically. Here we give two models that can be solved exactly, i.e., we can give the singularities in the complex time plane. The two models play a central role in quantum mechanics. Then we compare them with the numerical study of the nonlinear differential equation.

Reachability Analysis for Solvable Dynamical Systems

2018 ◽  
Vol 63 (7) ◽  
pp. 2003-2018 ◽  
Author(s):  
Ting Gan ◽  
Mingshuai Chen ◽  
Yangjia Li ◽  
Bican Xia ◽  
Naijun Zhan
Keyword(s):  
Dynamical Systems ◽  
Reachability Analysis ◽  
Solvable Dynamical Systems

Analytically solvable dynamical systems which are not integrable

1984 ◽  
Vol 13 (3) ◽  
pp. 339-356 ◽  
Author(s):  
Bruno Eckhardt ◽  
Joseph Ford ◽  
Franco Vivaldi
Keyword(s):  
Dynamical Systems ◽  
Solvable Dynamical Systems
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