scholarly journals Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform

2005 ◽  
Vol 46 (5) ◽  
pp. 053510 ◽  
Author(s):  
E. G. Kalnins ◽  
J. M. Kress ◽  
W. Miller
Keyword(s):  
Second Order ◽  
Two Dimensional ◽  
Conformally Flat ◽  
Superintegrable Systems

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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