Quantitative ergodic theorems and Diophantine approximation
We investigate the problem of Diophantine approximation on
surfaces using ergodic-theoretic techniques. It turns out that this problem
is closely related to the asymptotic distribution of orbits for a suitably
constructed dynamical system. Using this connection we establish
analogues of Khinchin's and Jarnik's theorems in our setting.
This is a joint work with A.Ghosh and A.Nevo.