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math.DS2025
On invariants of families of lemniscate motions in the two-center problem
Hanna Haeussler, Seongchan Kim
We determine four topological invariants introduced by Cieliebak-Frauenfelder-Zhao, based on Arnold's -invariant, of periodic lemniscate motions in Euler's two-center problem.
math.DS2024
Transverse foliations for two-degree-of-freedom mechanical systems
Naiara V. de Paulo, Seongchan Kim, Pedro A. S. Salomão +1
We investigate the dynamics of a two-degree-of-freedom mechanical system for energies slightly above a critical value. The critical set of the potential function is assumed to cont…