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arXiv · 1211.3397

Rescaling limits of complex rational maps

Jan Kiwi
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Abstract

We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space.It is shown that any given sequence of maps of degree $d \ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which are not postcritically finite. For quadratic rational maps, a complete description of the possible rescaling limits is given. These results are obtained employing tools from non-Archimedean dynamics.

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Jan Kiwi. 2012-11-14. Rescaling limits of complex rational maps. https://doi.org/10.1215/00127094-2916431

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