Integrable Deformations of Cluster Maps of Type \(D_{2N}\)

IF 1.2 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2026-02-05 DOI:10.1007/s11040-026-09545-3

Wookyung Kim

引用次数: 0

Abstract

In this paper, we extend one of the main results from our joint work [12] with Hone and Mase, in which we studied a deformed type \(D_{4}\) map, to the general case of type \(D_{2N}\) for \(N\ge 3\). This can be achieved through a “local expansion" operation, introduced in our joint work [7] with Grabowski and Hone. This operation involves inserting a specific subquiver into the quiver arising from the Laurentification of the deformed type \(D_{4}\) map. This insertion yields a new quiver, obtained through the Laurentification of the deformed type \(D_{6}\) map and thus enables systematic generalization to higher ranks \(D_{2N}\). We also study the degree growth of the deformed type \(D_{2N}\) map via the tropical method and conjecture that, for each N, the deformed map is integrable, as indicated by the algebraic entropy test, a criterion for detecting integrability in discrete dynamical systems.

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类型簇映射的可积变形 \(D_{2N}\)

在本文中，我们将我们与Hone和Mase的联合工作[12]中研究变形类型\(D_{4}\)映射的主要结果之一推广到\(N\ge 3\)类型\(D_{2N}\)的一般情况。这可以通过我们与Grabowski和Hone的联合工作[7]中引入的“本地扩展”操作来实现。此操作涉及将一个特定的子箭插入到由变形类型\(D_{4}\)映射的Laurentification产生的箭中。这个插入产生了一个新的颤动，通过变形类型\(D_{6}\)地图的Laurentification获得，从而可以系统地推广到更高的级别\(D_{2N}\)。我们还通过热带方法研究了变形型\(D_{2N}\)映射的度增长，并推测，对于每个N，变形映射是可积的，如代数熵检验所表明的那样，代数熵检验是检测离散动力系统可积性的准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.