INVARIANTS OF CHAOTIC HAMILTONIAN-SYSTEMS

The invariants of chaotic bounded Hamiltonian systems and their relati on to the solutions of the first variational equations of the equation s of motion are studied. We show that these invariants are characteriz ed by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series def ined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibili ty appears to apply.