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A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems

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Abstract

Here, we present some complements to theorems of R. Gerard and Y. Sibuya, on the convergence of multivariate formal power series solutions of nonlinear meromorphic Pfaffian systems. Their most known results concern completely integrable systems with non-degenerate linear parts, whereas we consider some cases of non-integrability and degeneracy.

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Funding

The first author was supported by the Russian Foundation for Basic Research (grant nos. 16-51-150005 and 17-01-00515).

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Authors and Affiliations

  1. Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, Russia

    Renat Gontsov

  2. Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow, Russia

    Renat Gontsov

  3. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Miusskaya sq. 4, Moscow, Russia

    Irina Goryuchkina

Authors
  1. Renat Gontsov
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  2. Irina Goryuchkina
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Correspondence to Renat Gontsov.

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Gontsov, R., Goryuchkina, I. A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems. J Dyn Control Syst 26, 149–158 (2020). https://doi.org/10.1007/s10883-019-09441-w

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  • DOI: https://doi.org/10.1007/s10883-019-09441-w

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