Local analytic reduction of families of diffeomorphisms |
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Authors: | P Bonckaert |
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Institution: | a Hasselt University, Agoralaan, B-3590 Diepenbeek, Belgium b University of Groningen, Johann Bernoulli Institute, PO Box 407, 9700 AK Groningen, The Netherlands |
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Abstract: | We study local analytic simplification of families of analytic maps near a hyperbolic fixed point. A particularly important application of the main result concerns families of hyperbolic saddles, where Siegel's theorem is too fragile, at least in the analytic category. By relaxing on the formal normal form we obtain analytic conjugacies. Since we consider families, it is more convenient to state some results for analytic maps on a Banach space; this gives no extra complications. As an example we treat a family passing through a 1:−1 resonant saddle. |
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Keywords: | Analytic normal form Families of hyperbolic saddles |
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