Geometrical objects and structures associated to some dynamical systems (II) (Q2919594)

This paper is a continuation of previous studies of the authors on dynamical systems \textit{V. Obădeanu} and \textit{M. Ciobanu} [An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 53, Suppl., 287--296 (2007; Zbl 1199.35042)]. The authors consider dynamical systems of first order partial differential equations, which describe the evolution of some deformable continuous media. To such a system, using the coefficients of the corresponding variational forms, it is possible to associate, canonically, a geometrical structure of metrical nature and a connection, a covariant derivative, a parallel transport and autoparallel manifolds such that the trajectories of the given system are autoparallels with respect to this structure. A second geometrical structure corresponds to the adjoint linear system of variational forms.