For certain finite groups $G$ of B\"acklund transformations we show that the dynamics $G$-invariant configurations $n|G|$ Calogero--Painlev\'e particles is equivalent to $n$-particle system. We also reduction on subset $n|G|\times n|G|$ matrix Painlev\'e system $n\times n$ The correspond folding equations. proofs are based Hamiltonian reductions.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 14 September 2020Accepted: 11 August 2021Published online: 16 December 2021KeywordsRiesz spectral operator, infinite-dimensional linear port-Hamiltonian system, strongly continuous groupAMS Subject Headings35P10, 47B06, 47D06, 35L40Publication DataISSN (print): 0363-0129I...

Port-Hamiltonian systems theory provides a structured approach to modelling, optimization and control of multiphysical systems. Yet, its relationship thermodynamics seems be unclear. The Hamiltonian is traditionally thought as energy, although meaning exergy. This insight yields benefits: 1. Links the GENERIC structure are identified, making it relatively easy borrow ideas from popular framewor...