Rigidity and Flexibility in Dynamics

Rigidity and Flexibility in Dynamics

Math 275 - MWF 10-11 pm - 232 SC
Harvard University - Fall 2006

Suggested Texts

J. Milnor, Dynamics in One Complex Variable , Third Edition. Princeton University Press, 2006.

Benedetti and Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, 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 187--188, Soc. Math. France 1990.

Other useful references

E. Ghys, Dynamique des flots unipotents sur les espaces homogènes, Sem. Bourbaki 1991/92; Asterisque 206.
H. Masur and S. Tabachnikov, Rational billiards and flat structures.
C. McMullen, From dynamics on surfaces to rational points on curves.
C. McMullen, Notes on Teichmüller Theory and Complex Dynamics
C. McMullen, Notes on Ergodic Theory
W. P. Thurston, Geometry and Topology of 3-Manifolds.

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 Rⁿ
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

Course home page: http://math.harvard.edu/~ctm/math275