Coalgebra symmetry for discrete systems

Abstract

In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are quasi-integrable and that all variational discrete quasi-radially symmetric systems in standard form are Poincaré--Lyapunov--Nekhoroshev maps of order $N-2$, where $N$ are the degrees of freedom of the system. We also discuss the integrability properties of several vector systems which are generalisations of well-known one degree of freedom discrete integrable systems, including two $N$ degrees of freedom autonomous discrete Painlevé I equations and an $N$ degrees of freedom McMillan map.

38 pages, 4 figures

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Cited by in corpus (4)

• 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
• Discrete-time systems in quasi-standard form and the ${\mathfrak{h}}_6$ coalgebra symmetry
• Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras