Trees and Superintegrable Lotka–Volterra Families

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-26 DOI:10.1007/s11040-024-09496-7

Peter H. van der Kamp, G. R. W. Quispel, David I. McLaren

引用次数: 0

Abstract

To any tree on n vertices we associate an n-dimensional Lotka–Volterra system with \(3n-2\) parameters and, for generic values of the parameters, prove it is superintegrable, i.e. it admits \(n-1\) functionally independent integrals. We also show how each system can be reduced to an (\(n-1\))-dimensional system which is superintegrable and solvable by quadratures.

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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.