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Misiurewicz maps unfold generically (even if they are critically non-finite)
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UNSPECIFIED (2000) Misiurewicz maps unfold generically (even if they are critically non-finite). FUNDAMENTA MATHEMATICAE, 163 (1). pp. 39-54. ISSN 0016-2736.
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Abstract
We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if f(lambda 0) is critically finite with non-degenerate critical point c(1)(lambda(0)),...,c(n)(lambda(0)) such that f(lambda 0)(ki) (c(i)(lambda(0))) = p(i)(lambda(0)) are hyperbolic periodic points for i = 1,..., n, then
lambda --> (f(lambda)(k1)(c(1)(lambda)) - p(1)(lambda),...,f(lambda)(kd-2) (c(d-2)(lambda)) - p(d-2)(lambda))
is a local diffeomorphism for lambda near lambda(0). For quadratic families this result was proved previously in [DH] using entirely different methods.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | FUNDAMENTA MATHEMATICAE | ||||
Publisher: | POLISH ACAD SCIENCES INST MATHEMATICS | ||||
ISSN: | 0016-2736 | ||||
Official Date: | 2000 | ||||
Dates: |
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Volume: | 163 | ||||
Number: | 1 | ||||
Number of Pages: | 16 | ||||
Page Range: | pp. 39-54 | ||||
Publication Status: | Published |
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