Abstract
We present a method to calculate numerically the action variables of a completely integrable Hamiltonian system with N degrees of freedom. It is a construction 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 independent irreducible paths on a given torus is turned into the problem of finding the lattice of zeros of an N-periodic function. This function is constructed using the flows of all constants of motion. Using the fact that neighbouring tori and their irreducible paths are related by some continuous deformation, a continuation method is constructed which allows a systematic scan of the actions. For N=2 we use a Poincare surface of section to define paths which cross neighbouring tori. Close to isolated periodic orbits the generators are either constructed explicitly or their asymptotic behaviour is given. As an example, the energy surface in the space of action variables of a Hamiltonian showing resonances is calculated.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
