Essential nonlinearity implied by symmetry group. Problems of affine invariance in mechanics and physics (Q765034)

The authors discuss the relations between the so-called essential nonlinearities (those which are not interpretable as some extra perturbations imposed on a linear background) and symmetries. They consider some discrete and continuous systems with large symmetry groups, and the mechanism of inducing nonlinearity by symmetry groups. The corresponding Noether theorem is also discussed as well as some important paradoxes that appear in the context of a bit exotic symmetries.