Normalization of rationally integrable systems

2018/03/13 by Nguyen Tien Zung, Zung, Nguyen Tien · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1803.04800

Abstract

In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincaré-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this analytic normalization result to the case of rationally integrable systems, where the first integrals and commuting vector fields are not required to be analytic, but just rational (i.e., quotients of analytic functions or vector fields by analytic functions).

Citations

• On differential equations in normal form

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• Local normal forms of dynamical systems with a singular underlying geometric structure

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