Andrew Clarke

most citedA counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes

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math.DS2023

Geodesics With Unbounded Speed on Fluctuating Surfaces

Andrew Clarke

We construct $C^{\infty}$ time-periodic fluctuating surfaces in $R^{3}$ such that the corresponding nonautonomous geodesic flow has orbits along which the energy, and thus t…

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…