On infinitesimal automorphisms of almost symplectic structures on tangent bundle of generalized Lagrangian space

Almost symplectic structure is defined on tangent bundle of generalized Lagrange space. It is proved that natural infinitesimal transformation is infinitesimal automorphism of almost symplectic structure if and only if it is infinitesimal motion of generalized Lagrange space. If arbitrary infinitesimal automorphism conserves certain linear connection and foliate structure then dimensionality of algebra Lie of automorphisms not exceed $n(3n+5)/2$, $n$ — dimensionality of basis manifold.