v 1 5 N ov 1 99 7 TWO - STRUCTURE FRAMEWORK FOR HAMILTONIAN DYNAMICAL SYSTEMS ∗

The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group of the order automorphisms (Lie algebras with invariant cones). Taking advantage of the reciprocal independence of the relevant structures, the inclusion relation between the two automorphism groups can be reversed; a procedure which leads to an entirely new formal language (ordered linear spaces with invariant Lie products). Presumably it offers an alternative description for quantum systems, radically different from the conventional algebraic models.