Hardy fields. (English) Zbl 0518.12014


12H20 Abstract differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
32B10 Germs of analytic sets, local parametrization
14Pxx Real algebraic and real-analytic geometry
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[1] Bellman, R., Stability Theory of Differential Equations (1953), McGraw-Hill: McGraw-Hill New York · Zbl 0052.31505
[2] Bourbaki, N., Fonctions d’une Variable Réele, (Étude Locale des Fonctions (1961), Hermann: Hermann Paris), Chapter V · Zbl 0346.26003
[3] du Bois-Reymond, P., Ueber asymptotische Werthe, infinitäre Approximationen und infinitäre Auflösung von Gleichungen, Math. Ann., 8, 362-414 (1875) · JFM 07.0249.01
[4] Hardy, G., Some results concerning the behaviour at infinity of a real and continuous solution of an algebraic differential equation of the first order, (Proc. London Math. Soc. Ser. 2, 10 (1912)), 451-468 · JFM 43.0390.02
[5] Hardy, G., Orders of Infinity (1924), Cambridge Univ. Press: Cambridge Univ. Press London/New York · JFM 50.0153.04
[6] Lightstone, A.; Robinson, A., Nonarchimedian Fields and Asymptotic Expansions (1975), North-Holland: North-Holland Amsterdam, and Amer. Elsevier, New York · Zbl 0303.26013
[7] Marić, V., Asymptotic behavior of solutions of a nonlinear differential equation of the first order, J. Math. Anal. Appl., 38, 187-192 (1972) · Zbl 0233.34066
[8] Olver, F., Asymptotics and Special Functions (1974), Academic Press: Academic Press New York · Zbl 0303.41035
[9] Robinson, A., On the real closure of a Hardy field, (Asser, G.; etal., Theory of Sets and Topology (1972), Deut. Verlag Wissenschaften: Deut. Verlag Wissenschaften Berlin) · Zbl 0298.02061
[10] Singer, M., Asymptotic Behavior of Solutions of Differential Equations and Hardy Fields, (Preliminary report (1976), SUNY: SUNY Stone Brook), unpublished
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