Dynamical and Computer-Assisted Methods Applied to Hamiltonian Systems

Lam, Wai Ting, Brooklyn NY

Investigators

Abstract

This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Wai-Ting Lam is awarded this fellowship to conduct a program of research and education at Florida Atlantic University (FAU) in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist J.D. Mireles-James. This is a research project aimed at the study of dynamics of some celestial mechanics models. In particular, the principal investigator (PI) will investigate a restricted four-body problem arising in modeling dynamics of a spacecraft or moonlet in a vicinity of a Jupiter Trojan asteroid. The PI will use variational methods to obtain realistic physical models for the gravitational potential of irregularly-shaped asteroids within certain families of shapes that are commonly used to model the shapes of asteroids. Along with this research, the PI will be involved in the activities to broaden participation of Underrepresented Minorities in mathematical sciences through the recruitment and retention of students at FAU, a Hispanic Serving Institution, as well as through collaboration with American Indian Science and Engineering society (Florida). In this project the PI will develop advanced numerical algorithms and computer assisted proofs that will lead to a more detailed, rigorous descriptions of the dynamics in a variety of realistic settings. Resonant orbits in the vicinity of an irregularly shaped body will be investigated, and periodic and quasi-periodic orbits, hyperbolic invariant manifolds, and transverse intersections between such manifolds will be obtained via rigorous computations. Such geometric structures will be used to prove the existence of trajectories whose energy undergoes a significant change over time, thus constituting a verification of the Arnold diffusion in a concrete model. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.