Cieliebak K., Eliashberg Y., Polterovich L.
Contact Orderability up to Conjugation
2017, vol. 22, no. 6, pp. 585–602
We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of noncompact contact manifolds, called convex at infinity.
Cieliebak K., Frauenfelder U., van Koert O.
Periodic Orbits in the Restricted Three-body Problem and Arnold’s $J^+$ -invariant
2017, vol. 22, no. 4, pp. 408-434
We apply Arnold’s theory of generic smooth plane curves to Stark – Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold’s $J^+$-invariant, we introduce invariants of periodic orbits in planar Stark – Zeeman systems and study their behavior.