Degenerately Integrable Systems

TL;DR

This paper explores degenerate integrability in Hamiltonian systems, providing examples and new results on relativistic spin Ruijsenaars and Calogero-Moser models, including their duality.

Contribution

It introduces new degenerate integrability results for relativistic spin Ruijsenaars and Calogero-Moser systems and establishes their duality.

Findings

Degenerate integrability of relativistic spin Ruijsenaars systems

Degenerate integrability of spin Calogero-Moser systems

Duality between these two models

Abstract

The subject of this paper is degenerate integrability in Hamiltonian mechanics. It starts with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the Kepler system, Casimir models, spin Calogero models, spin Ruijsenaars models, and integrable models on symplectic leaves of Poisson Lie groups. The new results are degenerate integrability of relativistic spin Ruijsenaars and Calogero-Moser systems and the duality between them.