We prove that the vanishing spheres of the Lefschetz pencils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplectomorphism group of the fiber. More precisely, ...

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk ...