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math.DS2023
A remark on the onset of resonance overlap
Jacques Fejoz, Marcel Guardia
Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We…
math.DS2023★ 1 cited
A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes
Andrew Clarke, Jacques Fejoz, Marcel Guardia
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger…