The 
	    


	    sl2(R)
	    
	   coalgebra symmetry and the superintegrable discrete-time systems

Gubbiotti, Giorgio; Latini, Danilo

doi:10.1088/1402-4896/acbbb2

Cited by 2 publications

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References 93 publications

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“…Note that in this reasoning the variational structure is not restrictive because we are interested in studying integrability. Note that this idea was already extended in [62] where a classification of a broader class of variational difference equations admitting coalgebra symmetry with respect of the sl 2 (R) Lie-Poisson algebra was presented.…”

Section: Discussionmentioning

confidence: 99%

Coalgebra symmetry for discrete systems

Gubbiotti

Latini

Tapley³

2023

J. Phys. A: Math. Theor.

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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.

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Section: Discussionmentioning

confidence: 99%

Coalgebra symmetry for discrete systems

Gubbiotti

Latini

Tapley³

2023

J. Phys. A: Math. Theor.

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Growth and Integrability of Some Birational Maps in Dimension Three

Graffeo

Gubbiotti

2023

Ann. Henri Poincaré

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Motivated by the study of the Kahan–Hirota–Kimura discretisation of the Euler top, we characterise the growth and integrability properties of a collection of elements in the Cremona group of a complex projective 3-space using techniques from algebraic geometry. This collection consists of maps obtained by composing the standard Cremona transformation $${{\,\textrm{c}\,}}_3\in {{\,\textrm{Bir}\,}}(\mathbb {P}^3)$$ c 3 ∈ Bir ( P 3 ) with projectivities that permute the fixed points of $${{\,\textrm{c}\,}}_3$$ c 3 and the points over which $${{\,\textrm{c}\,}}_3$$ c 3 performs a divisorial contraction. Specifically, we show that three behaviour are possible: (A) integrable with quadratic degree growth and two invariants, (B) periodic with two-periodic degree sequences and more than two invariants, and (C) non-integrable with submaximal degree growth and one invariant.

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The sl2(R) coalgebra symmetry and the superintegrable discrete-time systems

Cited by 2 publications

References 93 publications

Coalgebra symmetry for discrete systems

Coalgebra symmetry for discrete systems

Growth and Integrability of Some Birational Maps in Dimension Three

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