On higher order geometry and induced objects on subspaces

Marcela Popescu and Paul Popescu

Besides a theory of higher order Finsler and Lagrange spaces, a dual theory of higher order Hamilton spaces was only recentely studied using the bundles of accelerations. In this paper we investigate the possibility to use these ideas in a more general setting. A recursive definition of higher order bundles defined by an affine bundle E and a vector pseudo-field on E can be considered, obtaining the acceleration bundles as a particular case. The case of non-holonomic spaces is effectively studied. A dual theory between lagrangians and hamiltonians (via Legendre transformations) is considered using affine bundles. A canonical way to induce a hamiltonian on an affine subbundle is also given.