Abstract
Let F be an automorphism of which has an attracting fixed point. It is well known that the basin of attraction is biholomorphically equivalent to . We will show that the basin of attraction of a sequence of automorphisms f 1, f 2, . . . is also biholomorphic to if every f n is a small perturbation of the original map F.
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References
Bedford, E.: Open problem session of the biholomorphic mappings meeting at the American Institute of Mathematics Palo Alto, CA, 2000
Fornæss, J.E., Stensønes, B.: Stable manifolds of holomorphic hyperbolic maps. Internat. J. Math. 15(8), 749–758 (2004)
Jonsson, M., Varolin, D.: Stable manifolds of holomorphic diffeomorphisms. Invent. Math. 149(2), 409–430 (2002)
Peters, H., Wold, E.F.: Non-autonomous basins of attraction and their boundaries. J. Geom. Anal. 15, 123–136 (2005)
Rosay, J.-P., Rudin, W.: Holomorphic maps from C n to C n, Trans. Amer. Math. Soc. 310(1), 47–86 (1988)
Sternberg, S.: Local contractions and a theorem of Poincaré. Amer. J. Math. 79, 809–824 (1957)
Wold, E.F.: Fatou-Bieberbach domains. Internat. J. Math. 16, 1119–1130 (2005)