Example · Undergraduate
Terms
| Term | This example | Why |
|---|
| periodic orbit |
✓ |
The unit circle is a periodic orbit of the harmonic oscillator, because the solution $(\cos t, -\sin t)$ goes around the unit circle with period $2 \pi$.
|
| omega limit set |
✓ |
The unit circle is the ω-limit set of each of its own points, because the solutions on it go around it periodically.
|
| limit cycle |
✗ |
The unit circle is not a limit cycle of the harmonic oscillator, because every nearby circle is also a periodic orbit, so it is not isolated.
|
| attractive |
✗ |
The unit circle is not attractive for the harmonic oscillator, because nearby solutions stay on their own circles and do not approach it.
|
| attractor |
✗ |
The unit circle is not an attractor for the harmonic oscillator, because nearby solutions do not approach it.
|
Distinctions using this example
- Periodic orbit vs. limit cycle: The unit circle is a periodic orbit of the harmonic oscillator but not a limit cycle, because every circle around the origin is also a periodic orbit, so the unit circle is surrounded by other periodic orbits.
All examples · All distinctions · All definitions