# Dynamical Systems & Ergodic Theory

Dynamical systems are systems in motion, often governed by differential equations, but also perhaps by other continuous or discrete formulae. Ergodic theory is the study of statistical properties of that motion. Originally created to connect thermodynamics to statistical mechanics, it has been extended to connect with many branches of mathematics, including differential geometry and number theory. Members of our ergodic theory group do research on complex dynamics, nonsingular and measure preserving ergodic theory, symbolic dynamics, tiling dynamical systems, ergodic theorems, return times theorems, multiple recurrence, nonconventional ergodic averages, connections with analysis and probability theory, Lie group actions, and foliations.