We introduce a new family of Hamiltonians with a deformed Kepler–Coulomb potential
dependent on an indexing parameter k. We show that this family is superintegrable for all …

We design fast trajectories of a trap to transport two ions using a shortcut-to-adiabaticity
technique based on invariants. The effects of anharmonicity are analyzed first perturbatively …

We consider the general problem of motion of a rigid body about a fixed point under the
action of an axisymmetric combination of potential and gyroscopic forces. We will construct …

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum
(SAV) spacetimes that are constructed from a complex Ernst potential. Some of the …

We investigate integrable two-dimensional Hamiltonian systems with scalar and vector
potentials, admitting second invariants which are linear or quadratic in the momenta. In the …

arXiv:math/0406209v1 [math.DS] 10 Jun 2004 A new integrable system on the sphere Page 1
arXiv:math/0406209v1 [math.DS] 10 Jun 2004 A new integrable system on the sphere Holger …

In the present article, a new two-dimensional integrable system containing 17 free
parameters is introduced. For giving certain values for these parameters, new integrable …

A theorem is derived which determines higher order first integrals of autonomous holonomic
dynamical systems in a general space, provided the collineations and the Killing tensors–up …

We study strongly and weakly integrable 2-dimensional Hamiltonian systems with velocity
dependent potentials. We determine the set of conditions which must be satisfied in order to …

In this paper we construct a new integrable natural conservative mechanical system
admitting a second invariant of the fourth degree in velocities. This system is quite general …