25 citations · 44 across the 14 of their papers we have counts for
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Geodesics With Unbounded Speed on Fluctuating Surfaces
Andrew Clarke
We construct time-periodic fluctuating surfaces in such that the corresponding nonautonomous geodesic flow has orbits along which the energy, and thus t…
Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing arg…
Generic Properties of Geodesic Flows on Analytic Hypersurfaces of Euclidean Space
Andrew Clarke
Consider the geodesic flow on a real-analytic closed hypersurface of , equipped with the standard Euclidean metric. The flow is entirely determined by the manifol…
Arnold Diffusion in Multi-Dimensional Convex Billiards
Andrew Clarke, Dmitry Turaev
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with the velocity vector making a small positive angle with the boundary. Lazutkin pro…