The Integrable Mapping as the Discrete Group of Inner Symmetry of Integrable Systems

TL;DR

This paper demonstrates that integrable mappings are linked to hierarchies of integrable evolution equations that remain invariant under the transformations they generate.

Contribution

It establishes a connection between integrable mappings and hierarchies of integrable systems, revealing their role as discrete symmetries.

Findings

Integrable mappings correspond to invariant hierarchies of evolution equations.

Each integrable mapping is associated with a hierarchical integrable system.

The invariance under the mapping characterizes the integrability of the system.

Abstract

It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.