Geometric structures associated with certain dynamical systems
The author considers a system of implicit second-order ordinary differential equations \(F=0\) written in the main form, on an \(m\)-dimensional differentiable manifold \(M\). He associates to it a geometrical structure defined respectively on \(M\), on \(J_2(M)\) and on \(\operatorname {Ker} F\), the last being a differentiable submanifold of \(J_2(M)\). This is given by a distinguished tensor \(A_{ij}(t,x,y)\) and by a pair of special nonlinear connections. Finally an object of ``dissipativity'' is defined.
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