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In this paper we study some geometrical objects (d-tensors, multi-timesemisprays of polymomenta and nonlinear connections) on the dual 1-jet vectorbundle $J^{1*}(\cal{T}, M)\to \cal{T}\times M$. Some geometrical formulas,which connect the last two geometrical objects, are also derived. Finally, acanonical nonlinear connection produced by a Kronecker $h$-regular multi-timeHamiltonian is given.

Canonical Nonlinear Connections in the Multi-Time Hamilton Geometry