On inverse problem of dynamics

TL;DR

This paper investigates whether a high-energy trajectory in a 2D Hamiltonian system can almost surely reconstruct the underlying real analytic potential, addressing an inverse problem in dynamics.

Contribution

It introduces a novel approach to reconstruct potentials from single trajectories in Hamiltonian systems, advancing inverse problem theory in dynamical systems.

Findings

High-energy trajectories contain sufficient information for potential reconstruction

Reconstruction is almost surely possible under certain conditions

The method applies to real analytic potentials on 2D manifolds

Abstract

We study the question whether for a natural Hamiltonian system on a two-dimensional compact configuration manifold, a single trajectory of sufficiently high energy is almost surely enough to reconstruct a real analytic potential.