symmetry of a solution of an ordinary differential equation
then is called a symmetry of the solution of .
Let be a symmetry of the ordinary differential equation and be a periodic solution of . If
for a certain then is called a symmetry of the periodic solution of .
lemma: If is a symmetry of the ordinary differential equation and let be a solution(either steady state or periodic) of . Then is a solution of .
proof: If is a solution of implies . Let’s now verify that is a solution, with a substitution into . The left hand side of the equation becomes and the right hand side of the equation becomes since is a symmetry of the differential equation. Therefore we have that the left hand side equals the right hand side since . qed
- GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
|Title||symmetry of a solution of an ordinary differential equation|
|Date of creation||2013-03-22 13:42:26|
|Last modified on||2013-03-22 13:42:26|
|Last modified by||Daume (40)|
|Synonym||symmetry of a periodic solution solution of an ordinary differential equation|