Reappearance of Ordered Motion in NonIntegrable Hamiltonian Systems The Strong Coupling Case
Abstract
The reappearance of order from chaos in twodegreesoffreedom nonintegrable Hamiltonians is shown not to be restricted to specially coupled nonlinear systems which effectively decouple on increasing the energy. The numerical demonstration is with a class of pair potentials constructed from the sum of three exponential terms. The coupling in these systems remains strong for all energies. These necessary physical condition on the bounded total potential V_{T} for the reappearance of order is that in the limit of both small and large energy V_{T} tends to an integrable limit. As a consequence, at least two ordertochaos transition energies exist. A possible necessary condition on V_{T} is given which may decide whether chaos is small scale or global. It is conjectured that there may be a fine structure to the degree of chaos vs E curves.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 December 1982
 DOI:
 10.1143/PTP.68.1854
 Bibcode:
 1982PThPh..68.1854A