scholarly journals Complete symmetry group and nonlocal symmetries for some two-dimensional evolution equations

2009 ◽  
Vol 357 (1) ◽  
pp. 225-231 ◽  
Author(s):  
S.M. Myeni ◽  
P.G.L. Leach
Keyword(s):  
Symmetry Group ◽  
Evolution Equations ◽  
Two Dimensional ◽  
Nonlocal Symmetries ◽  
Complete Symmetry ◽  
Complete Symmetry Group

SET IDEALS WITH ISOMORPHIC SYMMETRY GROUPS

2002 ◽  
Vol 34 (1) ◽  
pp. 37-45
Author(s):  
PETER BIRYUKOV ◽  
VALERY MISHKIN
Keyword(s):  
Automorphism Group ◽  
Symmetry Group ◽  
Wide Class ◽  
Metric Spaces ◽  
Outer Automorphism ◽  
Symmetry Groups ◽  
Outer Automorphism Group ◽  
Complete Symmetry ◽  
Thin Sets ◽  
Complete Symmetry Group

A criterion of isomorphism for symmetry groups of set ideals is provided in terms of ideal quotients and cardinal invariants. Furthermore, set ideals with complete symmetry group are characterized. They form a wide class, comprising, for example, all uniform dense ideals and the ideals of ‘thin’ sets in separable metric spaces. If the symmetry group of a set ideal is not complete, then its outer automorphism group is shown to be cyclic of order 2.

scholarly journals The complete symmetry group of a forced harmonic oscillator

1980 ◽  
Vol 22 (1) ◽  
pp. 12-21 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Harmonic Oscillator ◽  
Symmetry Group ◽  
Lie Groups ◽  
Time Dependent ◽  
One Dimensional ◽  
Complete Symmetry ◽  
Point Transformations ◽  
The One ◽  
Dependent Point ◽  
Complete Symmetry Group

AbstractThe complete symmetry group of a forced harmonic oscillator is shown to be Sl(3, R) in the one-dimensional case. Approaching the problem through the Hamiltonian invariants and the method of extended Lie groups, the method used is that of time-dependent point transformations. The result applies equally well to the forced repulsive oscillator and a particle moving under the influence of a coordinate-free force. The generalization to na-dimensional systems is discussed.

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