Caratheodory convergence of immediate basins of attraction to a Siegel disk

Details Caratheodory convergence of immediate basins of attraction to a Siegel disk Caratheodory convergence of immediate basins of attraction to a Siegel disk

2006-08-25

arxiv.org/abs/math/0608644v4

Mathematics

Complex Variables

Example 2 in Section 3 is corrected, Theorem 3 and two refs are added

Scientific paper

Let f_n be a sequence of analytic functions in a domain U with a common attracting fixed point z_0. Suppose that f_n converges to f_0 uniformly on each compact subset of U and that z_0 is a Siegel point of f_0. We establish a sufficient condition for the immediate basins of attraction $\mathcal A^*(z_0,f_n,U)$ to form a sequence that converges to the Siegel disk of f_0 as to the kernel with respect to z_0. The same condition is shown to imply convergence of the Koenings functions associated with f_n to that of f_0. Our method allows us also to obtain a kind of quantitative result for analytic one-parametric families.

Affiliated with

Also associated with

No associations

Rating

Caratheodory convergence of immediate basins of attraction to a Siegel disk does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Caratheodory convergence of immediate basins of attraction to a Siegel disk, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Caratheodory convergence of immediate basins of attraction to a Siegel disk will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-111947