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arXiv · 1206.2376

On the asymptotic expansion of maps with disconnected Julia set

Juan Rivera-Letelier
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Abstract

We study the asymptotic expansion of smooth one-dimensional maps. We give an example of an interval map for which the optimal shrinking of components exponential rate is not attained for any neighborhood of a certain fixed point in the boundary of a periodic Fatou component. We prove a general result asserting that, when this happens the components do shrink exponentially, although the rate is not the optimal one. Finally, we give an example of a polynomial with real coefficients, such that all its critical points in the complex plane are real, and such that its asymptotic expansion as a complex map is strictly smaller than its asymptotic expansion as a real map.

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Juan Rivera-Letelier. 2012-06-11. On the asymptotic expansion of maps with disconnected Julia set. https://arxiv.org/abs/1206.2376

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