Miura maps for St\"{a}ckel systems

TL;DR

This paper introduces Miura maps between algebraic curves of hyperelliptic type, leading to a novel method for generating multi-Hamiltonian structures in St"{a}ckel systems, enhancing their integrability framework.

Contribution

The paper presents a new approach using Miura maps to connect algebraic curves and St"{a}ckel systems, enabling the construction of multi-Hamiltonian representations.

Findings

Miura maps induce transformations between St"{a}ckel systems.

New multi-Hamiltonian representations are constructed.

Provides a systematic method for generating integrable structures.

Abstract

We introduce the concept of Miura maps between parameter-dependent algebraic curves of hyperelliptic type. These Miura maps induce Miura maps between St\"{a}ckel systems defined (on the extended phase space) by the considered algebraic curves. This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems.