Bertrand's theorem states
Among central force potentials with bound orbits, there are only two types of central force potentials with the property that all bound orbits are also closed orbits, the inverse-square force potential and the harmonic oscillator potential.
Especially the notion of "closed orbits" reminds me of Lyapunov stability, a prominent concept of Chaos theory. Is there a connection between Bertrands theorem and Chaos theory? Can Bertrands theorem be derived using methods from Chaos theory?
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