## Institute for Mathematical Sciences

## Preprint ims91-4

** M. Rees**
* A Partial Description of the Parameter Space of Rational Maps of Degree Two: Part 2.*

Abstract: This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of
degree two, by concentrating on those varieties in which one
critical point is periodic. We prove some general results about
nonrational critically finite degree two branched coverings,
and finally identify the boundary of the rational maps in the
combinatorial model, thus completing the proofs of results
announced in Part 1.

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