Marcela Popescu and Paul Popescu

On higher order geometry and induced objects on subspaces


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.