## 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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### References:

 [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 [3] –, Surface transformations and their dynamical applications.Acta Math., 43 (1920), 1–119. (In particular p. 7.) · JFM 47.0985.03 [4] Bishop, E., Differentiable manifolds in complex Euclidean space.Duke Math. J., 32 (1965), 1–22. · Zbl 0154.08501 [5] Chern, S. S. &Moser, J. K., Real hypersurfaces in complex manifolds.Acta Math., 133 (1974), 219–271. · Zbl 0302.32015 [6] Freeman, M., Polynomial hull of a thin two-manifold.Pacific J. Math., 38 (1971), 377–389. · Zbl 0205.09401 [7] Hunt, L. R., The local envelope of holomorphy of ann-manifold inC n .Bol. Un. Mat. Ital., 4 (1971), 12–35. · Zbl 0212.42801 [8] Kenig, C. &Webster, S., The local hull of holomorphy of a surface in the space of two complex variables.Invent. Math., 67 (1982), 1–21. · Zbl 0489.32007 [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 [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
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