Poincaré section

A Poincaré section is a method used in the study of complex systems to analyze their behavior over time. Imagine tracking a moving object continuously; instead, you choose a specific surface or condition and record where the object intersects this surface each time. These intersection points help to reveal patterns or structures within the system's motion, such as periodicity or chaos. Essentially, it simplifies a complicated, ongoing process into a series of snapshots, making it easier to understand the system’s long-term behavior without analyzing every detail continuously.