Poincaré section

A Poincaré section is a way of looking at something called a “dynamical system”. A dynamical system is a system with different pieces which interact with each other by following some set of rules, like a game of chess.

A Poincaré section looks at the “points of intersection” between the pieces of the dynamical system. A point of intersection is where two pieces of the dynamical system – like two different pieces on a chess board – meet. By looking at the points of intersection, scientists can learn more about the system and how it works.

So, a Poincaré section is like taking a photograph of the dynamical system over and over again, from different angles and at different moments in time. By looking at all of these photographs together, scientists can learn more about the dynamical system and how it moves.