ordinary differential equation; ordinary difference equation; first integral; symmetry; infinitesimal symmetry; moving frame
The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.
 Olver, P. J.: Applications of Lie Groups to Differential Equations
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 Tryhuk, V., Chrastinová, V.: Equivalence of difference equations within the web theory. Mathematica Slovaca, to appear.