Ergodic theorems for dilates of submanifolds in R^d actions

Abstract: I will discuss the validity of pointwise ergodic theorems for dilates of submanifolds in R^d-actions. In particular, I will present two recent results in this direction. The first, joint work with P. Bandi and D. Kleinbock, provides a positive result for continuous test functions in mixing R^d-actions. The second, joint work with J. Cheng and B. Guo, shows that if the regularity assumption on the test function is removed, a pointwise theorem may fail to hold.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar