Discrete-time systems in quasi-standard form and the \mathfrakh₆ coalgebra symmetry

2024/10/29 by Drozdov, Pavel, Gubbiotti, Giorgio · 2 citations
#17B80 (Primary) 39A36 (Secondary) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2410.22434

Abstract

In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra \mathfrakh₆. The outcome of this study is a family of systems depending on an arbitrary function of three variables, playing the rôle of the potential. Moreover, using a direct search approach, we classify discrete-time systems from this family that admit an additional invariant at most quadratic in the physical variables. We discuss the integrability properties of the obtained cases, their relationship with known systems, and their continuum limits.

Cited by

• A novel chain of Lie algebras and its coalgebra symmetry
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models

Related

• Structural and Symmetry Analysis of Discrete Dynamical Systems
• Reflection groups and discrete integrable systems
• (Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
• Integrable Lattice Systems and Markov Processes
• Graded Lie algebras, representation theory, integrable mappings and systems