Andrew Clarke

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

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

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.DG2023

G $_{2}$ -instantons on $2$ -step nilpotent Lie groups

Andrew Clarke, Viviana del Barco, Andrés J. Moreno

We study the G $_{2}$ -instanton condition for a family of metric connections arisen from the characteristic connection, on $7$ -dimensional $2$ -step nilpotent Lie groups with left-inva…

math.DG2023

Semi-stability and local wall-crossing for hermitian Yang-Mills connections

Andrew Clarke, Carl Tipler

We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact Kähler manifold. Assuming the automorphism group of its graded object to be abelian, we provi…

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…

Geodesics With Unbounded Speed on Fluctuating Surfaces

G2​-instantons on 2-step nilpotent Lie groups

Semi-stability and local wall-crossing for hermitian Yang-Mills connections

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

G $_{2}$ -instantons on $2$ -step nilpotent Lie groups