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- W4300805211 abstract "Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is described. The method enables one to integrate a wide class of polynomial multi--particle dynamical systems. The general solutions of certain dynamical systems related to linear second--order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived. Our approach is also applicable to dynamical systems that are not multi--particle by their nature but that can be regarded as multi--particle (for example, the Darboux--Halphen system and its generalizations). A wide class of two and three--particle polynomial dynamical systems is integrated." @default.
- W4300805211 created "2022-10-04" @default.
- W4300805211 creator A5075563834 @default.
- W4300805211 creator A5090529274 @default.
- W4300805211 date "2014-07-07" @default.
- W4300805211 modified "2023-09-26" @default.
- W4300805211 title "Multi-particle dynamical systems and polynomials" @default.
- W4300805211 doi "https://doi.org/10.48550/arxiv.1407.1641" @default.
- W4300805211 hasPublicationYear "2014" @default.
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