## Institute for Mathematical Sciences

## Preprint ims92-14

** J. Milnor**
* Remarks on Quadratic Rational Maps*

Abstract: This will is an expository description of quadratic rational maps. Sections 2 through 6 are concerned with the geometry and
topology of such maps. Sections 7--10 survey of some topics
from the dynamics of quadratic rational maps. There are few
proofs. Section 9 attempts to explore and picture moduli space
by means of complex one-dimensional slices. Section 10
describes the theory of real quadratic rational maps.
For convenience in exposition, some technical details have been
relegated to appendices: Appendix A outlines some classical
algebra. Appendix B describes the topology of the space of
rational maps of degree \[d\]. Appendix C outlines several
convenient normal forms for quadratic rational maps, and
computes relations between various invariants.\break Appendix D
describes some geometry associated with the curves
\[\Per_n(\mu)\subset\M\]. Appendix E describes totally
disconnected Julia sets containing no critical points.
Finally, Appendix F, written in collaboration with Tan Lei,
describes an example of a connected quadratic Julia set for
which no two components of the complement have a common
boundary point.

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