Diophantine approximation for algebraic numbers
Hillel Furstenberg (The Hebrew University of Jerusalem)
MSRI: Simons Auditorium
A number is well approximable (WA) if the error when approximatin by p/q can be made small compared to the sqare of 1/q. Almost all reals are WA. For good reasons quadratic irrationals are not. Nothing is known for cubic irrationals. We show how this relates to special orbits in homogeneous dynamics.