Discrete-time systems in quasi-standard form and the ${\mathfrak{h}}_6$ coalgebra symmetry

Abstract

In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra ${\mathfrak{h}}_6$. 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.

34 pages, 2 tables

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Cited by in corpus (2)

• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Explicit isomorphisms for the symmetry algebras of continuous and discrete isotropic oscillators