Email this article Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
- Authors: Gontsov R.R.1,2, Goryuchkina I.V.3
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Affiliations:
- Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
- National Research University "Moscow Power Engineering Institute"
- Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
- Issue: Vol 210, No 9 (2019)
- Pages: 3-18
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/133280
- DOI: https://doi.org/10.4213/sm9064
- ID: 133280
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Abstract
A sufficient condition is proposed which ensures that a Dulac series that formally satisfies an algebraic ordinary differential equation (ODE) is convergent. Such formal solutions of algebraic ODEs are quite common: in particular, the Painleve III, V and VI equations have formal solutions given by Dulac series; they are convergent in view of the sufficient condition presented. Bibliography: 13 titles.
Keywords
About the authors
Renat Ravilevich Gontsov
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute); National Research University "Moscow Power Engineering Institute"
Email: gontsovrr@gmail.com
Candidate of physico-mathematical sciences, Associate professor
Irina Vladimirovna Goryuchkina
Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
Email: igoryuchkina@gmail.com
Candidate of physico-mathematical sciences, Senior Researcher
References
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