1. The generalized center problem of resonant infinity for a polynomial differential system
- Author
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Wu, Yusen and Zhang, Cui
- Subjects
- *
GENERALIZATION , *POLYNOMIALS , *HOMEOMORPHISMS , *MATHEMATICAL transformations , *NUMERICAL calculations , *ALGORITHMS , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: This paper explores the problems of generalized center conditions and integrability of resonant infinity for a complex polynomial differential system. The method is based on converting resonant infinity into an elementary singular point by a homeomorphic transformation. The calculation of generalized singular point quantities is an effective way of finding necessary conditions for integrable systems. A new recursive algorithm for computing generalized singular point quantities at the origin of the transformed system is derived. At the same time, a necessary and sufficient condition for resonant infinity to be a generalized complex center is presented. As an application of the new recursive algorithm, the generalized center conditions for resonant infinity for a class of cubic systems are discussed. To the best of our knowledge, this is the first time that the generalized center problem has been considered for resonant infinity. [Copyright &y& Elsevier]
- Published
- 2011
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