| 1. | In several cases, the existence of a periodic orbit was known.
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| 2. | After the bifurcation there is no longer a periodic orbit.
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| 3. | This is usually accompanied by the birth or death of a periodic orbit.
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| 4. | For other values of \ rho, the system displays knotted periodic orbits.
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| 5. | The trace formula asserts that each periodic orbit contributes a sinusoidal term to the spectrum.
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| 6. | Periodic-orbit theory gives a recipe for computing spectra from the periodic orbits of a system.
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| 7. | The set of points that never leaves the neighborhood of the given periodic orbit form a fractal.
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| 8. | Thus, a heteroclinic orbit can be understood as the transition from one periodic orbit to another.
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| 9. | Using the trace formula to compute a spectrum requires summing over all of the periodic orbits of a system.
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| 10. | Without these restrictions, no continuous time system with fixed points or periodic orbits could have been structurally stable.
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