Arithmetic Geometry
Ergodicity is a property of dynamical systems where, over a long period, the time spent by a system in a particular state is proportional to the volume of the state in phase space. This concept connects to the idea that average behavior over time reflects the overall structure of the system. In essence, ergodic systems exhibit predictable long-term statistical behavior that aligns with their invariant measures, making them significant in studying both dynamics and number theory.
congrats on reading the definition of ergodicity. now let's actually learn it.