Logarithm laws and shrinking target properties

Abstract

We survey some of the recent developments in the study of logarithm laws and shrinking target properties for various families of dynamical systems. We discuss connections to geometry, diophantine approximation, and probability theory.Comment: This is a survey paper written following the Conference on Measures and Dyanmics on groups and homogeneous spaces, at TIFR, Mumbai, in Dec. 2007. It is in honor of Prof. S.G. Dani's 60th Birthda