# Backlund transformations and divisor doubling

## TL;DR

This paper explores the use of divisor doubling techniques to construct new auto Bäcklund transformations for classical integrable systems like the Lagrange top and Hénon-Heiles system, enhancing methods for canonical transformations.

## Contribution

It introduces a novel application of divisor doubling to generate auto Bäcklund transformations for specific classical mechanical systems.

## Key findings

- New auto Bäcklund transformations for Lagrange top and Hénon-Heiles system
- Application of divisor doubling in classical mechanics transformations
- Enhanced methods for canonical transformations in integrable systems

## Abstract

In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construction canonical transformations preserving form of Hamiltonians. We consider application of a standard generic divisor doubling for construction of new auto B\"{a}cklund transformations for the Lagrange top and H\'{e}non-Heiles system separable in parabolic coordinates.