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Normal forms for real surfaces in \(C^ 2\) near tangents and hyperbolic surface transformations. (English) Zbl 0519.32015


MSC:

32V40 Real submanifolds in complex manifolds
32C05 Real-analytic manifolds, real-analytic spaces
32H99 Holomorphic mappings and correspondences
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[1] Bedford, E. & Gaveau, B., Envelopes of holomorphy of certain 2-spheres in C2. To appear inAmer. J. Math., 105 (1983). · Zbl 0535.32008
[2] Birkhoff, G. D., The restricted problem of three bodies.Rend. Circ. Mat. Palermo, 39 (1915), 265–334. (In particular p. 310 and p. 329.) · JFM 45.1396.01 · doi:10.1007/BF03015982
[3] –, Surface transformations and their dynamical applications.Acta Math., 43 (1920), 1–119. (In particular p. 7.) · JFM 47.0985.03 · doi:10.1007/BF02401754
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[9] Lewy, H., On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables.Ann. of Math., 64 (1956), 514–522. · Zbl 0074.06204 · doi:10.2307/1969599
[10] Moser, J., On the integrability of area-preserving Cremona mappings near an elliptic fixed point.Boletin de la Sociedad Matematica Mexicana (2) 5 (1960), 176–180. · Zbl 0121.31404
[11] Siegel, C. L. & Moser, J. K.,Lectures on Celestial Mechanics. Springer, 1971. (In particular, p. 166ff.) · Zbl 0312.70017
[12] Siegel, C. L., Vereinfachter Beweis eines Satzes von J. Moser.Comm. Pure Appl. Math., 10 (1957), 305–309. · Zbl 0078.37504 · doi:10.1002/cpa.3160100301
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