Efficient Calculation of Actions H.R. Dullin A. Wittek Institut f¨ ur Theoretische Physik Universit¨ at Bremen Postfach 330440 28344 Bremen, Germany Phone: +49(0)421-218-2341 Fax: +49(0)421-218-4869 Email: hdullin or awittek@theo.physik.uni-bremen.de August 19, 1993 Abstract We present a method to numerically calculate the action variables of a com- pletely integrable Hamiltonian system with N degrees of freedom. It is a con- structification of the Liouville-Arnol’d theorem for the existence of tori in phase space. By introducing a metric on phase space the problem of finding N inde- pendent irreducible paths on a given torus is turned into the problem of finding the lattice of zeroes of an N -periodic function. This function is constructed us- ing the flows of all constants of motion. For N = 2 we use a Poincar´ e surface of section to scan all tori with a continuation method. As an example the energy surface in the space of action variables of a Hamiltonian showing resonances is calculated. Keywords: Hamiltonian Systems, Integrable Systems, Actions, Numerics PACS number: 0320 1