# Non-autonomous Henon-Heiles system from Painleve class

## TL;DR

This paper demonstrates how to deform a separable Henon-Heiles system, linked to the 5th-order KdV, into non-autonomous Painleve-type systems using isomonodromic Lax representations, revealing new connections between integrable systems.

## Contribution

It introduces a method to deform integrable Henon-Heiles systems into Painleve-type systems via isomonodromic Lax representations, expanding the understanding of their integrability properties.

## Key findings

- Deformation of Henon-Heiles system into Painleve-type systems.
- Connection established between KdV stationary flow and Painleve equations.
- Use of isomonodromic Lax representation for non-autonomous systems.

## Abstract

We show how to deform separable Henon-Heiles system with isospectral Lax representation, related with the stationary flow of the $5th$-order KdV, to respective non-autonomous systems of Painleve type with isomonodromic Lax representation.