Hamiltonian systems form the bedrock for modelling a vast range of physical phenomena, from celestial mechanics to quantum dynamics. Their evolution is governed by a Hamiltonian function that ...

Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

We use foliations and connections on principal Lie groupoid bundles to prove various integrability results for Lie algebroids. In particular, we show, under quite general assumptions, that the ...