Separation of variables for the generalized Henon-Heiles system and system with quartic potential

TL;DR

This paper develops a geometric method to find variables of separation for two integrable systems, the generalized Henon-Heiles system and a quartic potential system, enhancing understanding of their integrability.

Contribution

It introduces a geometric approach using natural Poisson bivectors to construct separation variables for these systems, providing new insights into their integrability.

Findings

Successful construction of separation variables for both systems

Detailed geometric framework for variable separation

Enhanced understanding of integrability in these systems

Abstract

We consider two well-known integrable systems on the plane using the concept of natural Poisson bivectors on Riemaninan manifolds. Geometric approach to construction of variables of separation and separated relations for the generalized Henon-Heiles system and the generalized system with quartic potential is discussed in detail.