Orateur
Mitsuhiro Shishikura
Description
When a family of rational maps degenerates, certain parametrized coordinate changes may give rise to a non-trivial return map. J. Kiwi studied such scaling limits for quadratic rational maps and M. Arfeux defined trees of spheres’’ for the degeneration. We will discuss a converse problem which means a construction of degeneration family from a given data, and its relation to the Berkovich space of the extension of the field of Laurent series. This can be considered as aspider algorithm’’ in the Berkovich space.
This is a unfinished work in progress with Arfeux and Kiwi, and some work-out examples with E. Hironaka related to Per_n(0) and Rohini Ramadas.
