ON THE BIGTH OF PB-CHAINS FOR GENERAL AREA-PRESERVING MAPS

A PB-chain(Poincare-Birkhoff chain) is by definition a pair of elliptic and hyperbolic n-periodic orbits for a mapping and its existence has been well established numerically or analytically in many particular occasions such as in standard maps or twist maps [1, 8, 9] or Henon maps [1, 2, 12]. This paper gives focus on the investigaton of the appearance of such a PB-chain in a one-parameter family of general area-preserving maps and is in fact a generalization of the results given in [12] for a one-parameter family of specific area-preserving maps, so called Henon maps.