Dynamical systems and ergodic theory Concept
Periodic orbit
Summary
Let a point that is not an equilibrium return to itself after a fixed positive time. Its orbit is a periodic orbit of the dynamical system. For an autonomous differential equation, it is the closed curve traced by a non-constant periodic solution. See the definition.
Where this leads
17 pages build on this one.
- Hopf bifurcation
- Bendixson–Dulac theorem
- Failure of Kalman's conjecture
- Crisis
- Failure of Aizerman's conjecture
- Non-wandering set
- Recurrent point
- Intermittency
- Floer homology
- Relaxation oscillation
- Poincaré map
- Weinstein conjecture
- Shilnikov theorem
- Peixoto's theorem
- Periodic solution
- Jakobson's theorem
- Singer's theorem
Further reading
- Web https://en.wikipedia.org/wiki/Periodic_point, Dynamical system
About this page
| Tag | 0AA97XA70K |
|---|---|
| URI | m2://0AA97XA70K |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37C27 |
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Definitions
Used by
- Hopf bifurcation
- Bendixson–Dulac theorem
- Failure of Kalman's conjecture
- Crisis
- Non-wandering set
- Recurrent point
- Intermittency
- Floer homology
- Relaxation oscillation
- Poincaré map
- Weinstein conjecture
- Shilnikov theorem
- Peixoto's theorem
- Periodic solution
- Singer's theorem