Syllabus
Complex Dynamics and Hyperbolic Geometry
Math 275  MWF 12:001:00 pm  216 Science Center
Harvard University  Spring 2000
Instructor:
Curtis T McMullen
(ctm@math.harvard.edu)
Texts
 Benedetti and Petronio.
Lectures on Hyperbolic Geometry.
SpringerVerlag, 1992.
 Bedford, Keane and Series.
Ergodic Theory, Dynamics and Hyperbolic Surfaces.
Oxford University Press, 1991.
 Carleson and Gamelin.
Complex Dynamics.
SpringerVerlag, 1993.
 Milnor.
Lectures on Complex Dynamics.
Vieweg, 1999. Distributed by the AMS.
 Otal.
Le théorème d'hyperbolisation pour
les variétés fibrées
de dimension trois
, Astérisque volume 235 (1996).
Distributed by AMS.
 Thurston.
Geometry and Topology of 3Manifolds.
Mimeographed notes, Princeton, 1979.
Prerequisites.
Intended for advanced graduate students.
Acquaintance with complex analysis, hyperbolic
geometry, Lie groups and dynamical systems
will be useful.
Topics.
We will discuss
hyperbolic 3manifolds and iterated rational maps
in relation to topology, analysis, Teichmüller theory and
ergodic theory.
Topics may include:

Hyperbolic manifolds

Ergodic theory on groups

Mixing of the geodesic flow

Quasiconformal maps

Mostow rigidity

Ahlfors' finiteness theorem

Bers' area theorem

Bounds on cusps

No invariant line field theorem (Sullivan)

Thickthin decomposition

Geometrically tame ends (Bonahon, Thurston)

The Ahlfors measure zero conjecture

Rational maps

Classification of stable regions

Nowanderingdomains theorem (Sullivan)

Holomorphic motions and stability

Invariant line fields and the
hyperbolicity conjecture

Bounds on indifferent cycles (Epstein)

Local connectivity and measure of the Julia set
(Branner, Hubbard and Yoccoz)
Additional References

Beardon.
The Geometry of Discrete Groups.
SpringerVerlag, 1983.
 Gardiner.
Teichmüller Theory and Quadratic Differentials.
Wiley Interscience, 1987.
 Imayoshi and Taniguchi.
Introduction to Teichmüller Spaces.
SpringerVerlag, 1992.

McMullen.
Complex Dynamics and Renormalization .
Annals of Math Studies 135, Princeton University Press, 1994.
 McMullen.
Renormalization and 3Manifolds which Fiber over the Circle.
Annals of Math Studies 142, Princeton University Press, 1996.
 Ratcliffe.
Foundations of Hyperbolic Manifolds.
SpringerVerlag, 1994.
 Sullivan.
On the ergodic theory at infinity of an arbitrary discrete group of
hyperbolic motions.
In: Kra and Maskit, editors, Riemann Surfaces and Related
Topics: Proceedings of the 1978 Stony Brook Conference.
Annals of Math. Studies 97, Princeton, 1981.
