Arnold's J^+-invariant in Hamiltonian dynamics

• Applicant: Professor Dr. Urs Frauenfelder
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 531257519

Periodic orbits play a crucial role macroscopically in celestial mechanics as well as microscopically in the dynamics of atoms. Usually periodic orbits appear in families. The shape of a periodic orbit in a family however can change drastically, so that it is in general very hard to tell if two periodic orbits belong to the same family or not. The goal of the project is to study invariants which do not change in a family of periodic orbits and compute these in important examples in celestial mechanics and quantum mechanics.

• DFG Programme: Research Grants