Concept
Integrability
The property of a dynamical system that enough conserved quantities exist to confine each trajectory to a low-dimensional set. An integrable system's orbits are orderly and describable in closed form; the typical system has no such quantities.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Adding up rectangles until they stop being rectangles
The integral is defined as a limit of sums of rectangles. The definition is exact, the picture is honest about what it costs, and the gap between them is the whole subject.
A bounce is a fold of the table
Reflect the room instead of the ball and every bounce disappears — the trajectory becomes a straight line through a tiled plane, and questions about what a ball does forever become questions about the slope of that line.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaBilliardsCausticConvergenceDirichletDirichlet's functionEquidistributionFundamental theoremIrrational rotationLebesgue integralLimitPeriodic orbit