Consider an ODE and the definition of generalized symmetry of an ODE. A generalized symmetry is called a nonlocal symmetry if the coefficients depend upon integral or multiple integrals. My best reference for the moment is @govinder1995determination...
Related: covering system. Symmetries of the covering system give rise to nonlocal symmetries of the covered system.
Interesting reference: calibre [AdamNonlocal98]. It appears what I talked with Paola, Conchi and Adrián.
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Author of the notes: Antonio J. Pan-Collantes
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