Rigidity and Flexibility in Dynamics

Math 275 - MWF 10-11 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, 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 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.

    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