ON THE MAPPING OF JET SPACES

Abstract

Any locally invertible morphism of a finite-order jet space is either a prolonged point transformation or a prolonged Lie's contact transformation (the Lie–Bäcklund theorem). We recall this classical result with a simple proof and moreover determine explicit formulae even for all (not necessarily invertible) morphisms of finite-order jet spaces. Examples of generalized (higher-order) contact transformations of jets that destroy all finite-order jet subspaces are stated with comments.

Keywords:

• Infinite-order jet spaces
• morphisms of jets
• generalized contact transformations
• Lie–Bäcklund theorem