On auto and hetero Backlund transformations for the Henon-Heiles systems

TL;DR

This paper explores the use of canonical transformations in parabolic coordinates as a means to generate auto and hetero Bäcklund transformations for the integrable Hénon-Heiles systems, providing new insights into their structure.

Contribution

It introduces a novel approach linking canonical transformations to Bäcklund transformations in the context of Hénon-Heiles systems.

Findings

Establishes a correspondence between canonical transformations and Bäcklund transformations.

Provides a framework for generating new solutions of Hénon-Heiles systems.

Enhances understanding of integrability through transformation techniques.

Abstract

We consider a canonical transformation of parabolic coordinates on the plain and suppose that this transformation together with some additional relations may be considered as a counterpart of the auto and hetero B\"acklund transformations associated with the integrable H\'enon-Heiles systems.