Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field

Hayato Chiba

研究成果: Contribution to journalArticle査読

5 被引用数 (Scopus)

抄録

Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous polynomial system of differential equations are studied by means of a weighted projective space and dynamical systems theory. A necessary and sufficient condition for the series solution to be a convergent Laurent series is given, which improves the well-known Painlevé test. In particular, if a given system has the Painlevé property, an algorithm to construct Okamoto's space of initial conditions is given. The space of initial conditions is obtained by weighted blow-ups of the weighted projective space, where the weights for the blow-ups are determined by the Kovalevskaya exponents. The results are applied to the first Painlevé hierarchy (2. m-th order first Painlevé equation).

本文言語英語
ページ(範囲)7681-7716
ページ数36
ジャーナルJournal of Differential Equations
259
12
DOI
出版ステータス出版済み - 12 15 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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