Linked from

The 12 pages that link to Periodic orbit, each with the reason it gives.

• Poincaré mapRelated: Each periodic orbit produces a periodic point of the return map.

• Lorenz systemCompared with: Lorenz trajectories in the chaotic regime do not settle into a repeating cycle.

• Periodic boundary conditionCompared with: It describes repetition in time, not a boundary constraint identifying spatial edges.

• Limit cycleNarrower topic: Every limit cycle is periodic, but only an isolated periodic orbit is a limit cycle.

• Action-angle variablesRelated: The closed cycles of periodic motion supply the integrals defining actions.

• Floquet theoryRelated: Linearizing near such an orbit yields a periodic system whose stability can be tested with Floquet multipliers.

• Poincaré–Bendixson theoremBroader topic: This is the possible non-equilibrium compact limit set guaranteed by the theorem.

• Bendixson–Dulac theoremBroader topic: The theorem’s contradiction argument assumes such an orbit bounds a region.

• Mary CartwrightRelated: Periodic forcing raised questions about repeating motions and their stability.

• Edge of chaosCompared with: Periodic motion provides a clear ordered alternative to chaotic behavior.

• Poincaré–Birkhoff theoremRelated: Fixed points of a Poincaré map correspond to periodic trajectories of the flow.

• Chaos and nonlinear dynamicsCompared with: Periodic motion is ordered repetition, one alternative to aperiodic chaotic behavior.