Poincaré map
Orbit intersection plot
A Poincaré map is a technique in dynamical systems for reducing continuous motion to discrete points by recording where a trajectory repeatedly crosses a chosen surface.
Named after mathematician Henri Poincaré, this tool transforms the study of complex orbits into analysis of simpler sequences of intersection points.
The Poincaré map revealed the system's periodic behavior.
It is especially useful for detecting chaos, periodicity, and stability in oscillating systems.
- attractorConvergence point for systems
- recurrenceReturn of something previous
- transversalLine crossing multiple others
- iterationRepeated procedural pass
- fixed pointValue unchanged by function
flow · periodicity · stroboscopic · chaos theory · bifurcation · section · trajectory · Lyapunov exponent · topology · stability · mathematics · initial conditions · foliation · manifold · pendulum · invariant · chaos · basin
Poincaré mapvector field
Function assigning directions to points