New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves

Abstract

For cubic pencils we define the notion of an involution curve. This is a curve which intersects each curve of the pencil in exactly one non-base point of the pencil. Involution curves can be used to construct integrable maps of the plane which leave invariant a cubic pencil.

References in corpus (2)

• Manin involutions for elliptic pencils and discrete integrable systems
• Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings

Cited by in corpus (2)

• Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings
• Classification of integrable boundary equations for integrable quad-graph systems