Rigidity and Flexibility in Dynamics
Math 275  MWF 1011 pm  232 SC
Harvard University  Fall 2006
Instructor:
Curtis T McMullen
Suggested Texts
J. Milnor,
Dynamics in One Complex Variable ,
Third Edition. Princeton University Press, 2006.
Benedetti and Petronio,
Lectures on Hyperbolic Geometry,
SpringerVerlag, 1992.
M. B. Bekka and M. Mayer,
Ergodic theory and topological dynamics of group actions on homogeneous spaces,
Cambridge University Press, 2000.
S. Tabachnikov,
Billiards ,
Soc. Math. France, 1995
W. Parry and M. Pollicott,
Zeta Functions and the Periodic Orbit Structure
of Hyperbolic Dynamics,
Astérisque 187188, Soc. Math. France 1990.
Other useful references
Prerequisites.
Intended for advanced graduate students.
Description
A survey of methods, results and open problems in
complex dynamics, hyperbolic geometry, and the ergodic
theory of Lie groups. Topics may include:
 Mostow rigidity
 Iterated rational maps
 Hausdorff dimension and the thermodynamic formalism
 Flows on homogeneous spaces
 Rational maps with given combinatorics
 Curves in moduli spce
 Billiards
 Dynamics on algebraic surfaces
 Lattices in R^{n}
 Higher rank actions
Grades.
Enrolled students should attend the course regularly.
Those taking the course for a grade will be asked to hand in
homework.
Calendar.
18 Sept (M)  First class 
9 Oct (M)  Columbus day  no class 
10 Nov (F)  Veteran's day  no class 
24 Nov (F)  Thanksgiving  no class 
18 Dec (M)  Last class 
2 Jan (Tu)  Reading period begins 
12 Jan (F)  Exams begin 
