Complementarity, duality and symmetry in nonlinear mechanics: GENERALIZED LEGENDRE-FENCHEL TRANSFORMATION

摘要

The aim of the paper is to characterize transformations that preserve the potential structure of a relationship between dual variables. The first step consists in "geometrizing" the condition for the existence of a potential. Having at hand this formulation, it becomes clear that the canonical similitudes represents the class of transformations that preserves the potential form of a relationship. Next, we derive the conditions under which canonical similitudes preserve the convexity of the potential or change it into concavity, This new class of transformations provides a generalization of the Legendre-Fenchel transformation.