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arXiv · 2109.10391

Coalgebra symmetry for discrete systems

G. Gubbiotti·D. Latini·B. K. Tapley
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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 Poincar\'e--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 Painlev\'e I equations and an $N$ degrees of freedom McMillan map.

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BibTeXRIS

G. Gubbiotti, D. Latini, B. K. Tapley. 2021-09-21. Coalgebra symmetry for discrete systems. https://doi.org/10.1088/1751-8121%2Facc992

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