Coalgebra symmetry for discrete systems
/ Authors
/ 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.
Journal: Journal of Physics A: Mathematical and Theoretical