There are many different approaches to geometrical symmetries 
(also called Lie point symmetries)of ordinary differential equations. 
For example [Olv, Steph, BluKu], they may be considered as parametrized 
transformations that for each value of parameter preserves 
equations manifold or kernel of differential operator associated with 
it or map each integral curve of the equation onto another one. We (are)(will be) 
especialy interested in the last point of view as it allows to join
results and applications connected with motion of curves in a plane 
[cf. ?????????]. 



Namely


  His whole approach