My area of interest is dynamical systems. I have done work on polygonal billiards and dynamics of flows on Teichmüller space; analysis of algorithms; and diffeomorphisms of surfaces. I am currently working on complex dynamics in two dimensions.
- Ergodicity of billiard flows and quadratic differentials (with S. Kerckhoff and H. Masur), Annals of Mathematics 124 (1986), 293–311.
- Polynomial diffeomorphisms of C2 VI: connectivity of J (with E. Bedford), Annals of Mathematics, 148 (1998), 695–735.
- Polynomial diffeomorphisms of C2 VII: hyperbolicity and external rays (with E. Bedford), Ann. Scient. Ec. Norm. Sup. 4 (32) (1999), 455–497.
- The dynamics of billiard flows in rational polygons; in Encyclopedia of Mathematical Sciences, vol. 100 (edited by Yu. Sinai), Springer-Verlag, 1999.
- Billiards on rational-angled triangles (with R. Kenyon), Comment. Math. Helv. 75 (2000), 65–108.
- Dynamics in Two Complex Dimensions; in Proceedings of the International Congress of Mathematicians, Beijing 2002, Vol. III: Invited Lectures, Higher Education Press, Beijing 2002, pp. 373–382.
- Real polynomial diffeomorphisms with maximal entropy: tangencies (with E. Bedford), Annals of Mathematics 160 (2004), 1–26.