Abstract

Full measure results for the most simple type of shrinking target and recurrence sets bring together two pillar stones in Ergodic theory; the Ergodic Theorem and Poincare Recurrence. The study of both sets in their full generality is motivated by results in Diophantine Approximation, but has applications in many areas such as Transcendental Dynamics. This talk will discuss sufficient conditions on dynamical systems that lead to a zero-one law for the shrinking target set. We also consider applications of the zero-one law; such as the frequency of strings of integers occurring in the base b expansion of real numbers. Time permitting, we will end by briefly looking at why obtaining a zero-one law for the recurrence set is more complex.

This talk does not assume any prior knowledge of dynamical systems.