A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New electromagnetic curvature defined via Jacobi-Maupertuis, showing positive curvature for non-zero magnetic force.
The paper explores transformations between power law problems and geodesics on cones.
Consider the equal mass planar -body problem with a potential corresponding to an inverse \textit{cube} force. The Jacobi-Maupertuis principle reparametrizes the dynamics as geodesics of a certain metric. We examine the curvature of this geodesic flow in the reduced space on the collinear and parallelogram invariant…
In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the -body problem with general masses and any potential with . We also observe dynamical consequences of these curvature values for relati…
We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is where is the triangle's moment of inertia and its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier p…
Marchal's lemma is the basic tool for eliminating collisions when using the direct method of the calculus of variations to establish existence of "designer" solutions to the classical N-body problem. Our goal here is to understand why Marchal's lemma holds, by taking a metric geometry perspective and employing the Jaco…
The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove…