Canonical Nonlinear Connections in the Multi-Time Hamilton Geometry

In this paper we study some geometrical objects (d-tensors, multi-time semisprays of polymomenta and nonlinear connections) on the dual 1-jet vector bundle $J^{1\ast }(\mathcal{T},\mathcal{M})\to \mathcal{T}\times \mathcal{M}$. Some geometrical formulas, which connect the last two geometrical objects, are also derived. Finally, a canonical nonlinear connection produced by a Kronecker $h$-regular multi-time Hamiltonian is given.