Construction of complex invariants for classical dynamical systems

With a view to extracting some further insight into the features of a dynamical system, we investigate here the possibility of its admitting complex dynamical invariants. For this purpose, both the rationalization and the bit algebraic methods are employed to study the one-dimensional Hamiltonian systems on the extended complex phase plane characterized by x = x(1) + ip(2), p = p(1) + ix(2). Several systems (including the PI-symmetric ones) are found to admit complex invariants. These invariants are expected to play an important role in the analysis of complex trajectories in both the classical and quantum mechanics of the system concerned. (C) 2001 Academic Press.