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A general background of higher order geometry and induced objects on subspaces. (English) Zbl 1054.53046

In this paper, the authors perform a recursive definition of higher-order bundles defined by an affine bundle \(E\) and a vector pseudo-field on \(E\). Also, they consider a dual theory between Lagrangians and Hamiltonians via Legendre transformations. A canonical way to induce a Hamiltonian on an affine subbundle is also given.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
58A20 Jets in global analysis
44A15 Special integral transforms (Legendre, Hilbert, etc.)
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
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