Do All Automorphisms in Physics Imply Symmetries in Equations?

[Garrulo]

All the physical simmetries implicate an automorphism in axioms. But ¿all the automorphisms from a physical equation do implicate a simmetry?

 

[Geofleur]

I am not sure I understand, but I think I may know what you have in mind. Many phenomena in physics are governed by differential equations, and we can consider an isomorphism of the solution set of a given equation into itself (an automorphism). Usually such an isomorphism expresses a coordinate transformation of some sort. This transformation maps solutions into each other, and the form of the governing differential equation does not change. We define such a map as a symmetry of the differential equation.