Symplectic Dynamics, Celestial Mechanics and Magnetism

• Applicants: Professor Dr. Luca Asselle; Professor Dr. Umberto Hryniewicz, Ph.D.; Professor Dr. Agustin Moreno
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566804407

Magnetic geodesic flows and mechanical systems with a potential are instances of a larger family of Hamiltonian dynamical systems called here electromagnetic. Relevant systems which are a mix of both appear in celestial mechanics, for instance, the circular restricted 3-body problem (CR3BP). Despite their commonalities, somewhat different methods have been shown to be effective in the study of one class rather than the other (magnetic versus mechanical). The overarching theme of the present project is to explore dynamical applications of the various available methods, with a unified viewpoint. The goals of the project, many of which are of practical interest, include: i) use curvature to obtain a better understanding of the dynamical properties as well as the contact geometry of magnetic systems below the Mane critical value, ii) find quantitative conditions for right-handedness for geodesic and magnetic flows on the two-sphere, iii) obtain new insight in the stability properties of relative equilibria using curvature, iv) obtain dynamical information about the spatial CR3BP (existence of periodic orbits, invariant sets, etc.) using holomorphic curves and/or curvature, v) address the existence of homoclinic connections for the Lyapounov orbit(s) in specific regimes of the planar CR3BP by building finite energy foliations, vi) carry out numerical studies of periodic orbits, and their bifurcations, of the CR3BP in connection to space mission design.

• DFG Programme: Research Grants