On asymptotic integrations of
Po Fang Hsieh (1978)
Archivum Mathematicum
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Po Fang Hsieh (1978)
Archivum Mathematicum
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Jean-Pierre Ramis, Yasutaka Sibuya (1994)
Annales de l'institut Fourier
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We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation the idea of our proof is to interpret...
Mami Suzuki (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Monique Hakim (1994)
Publicacions Matemàtiques
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Let F be a germ of analytic transformation of (C, 0). We say that F is semi-attractive at the origin, if F' has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C and F - Id has multiplicity k at the origin. This work has been inspired by two...
Aldo Andreotti, Alan Huckleberry (1972)
Compositio Mathematica
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