ON THE PADE APPROXIMATIONS TO THE BIRKHOFF-GUSTAVSON NORMAL-FORM

We demonstrate the efficiency of the Pade approximations to the Birkho ff-Gustavson normal form and to the associated formal integrals of mot ion for the case of the Henon-Heiles system. The accuracy of the forma l integrals of motion in the regular regions where invariant tori exis t is vastly improved, with the tendency that the poles of Pade approxi mations are located in the chaotic regions of the surface of section. The special case of the integrable Henon-Heiles system is an excellent example showing that here the poles of the Pade approximations are lo cated in classically forbidden regions. The 14th-order formal integral does not yet agree with the exact (numerical) surface of section, whi lst its [5, 5] Pade approximation does (within the limits of graphical resolution). These findings re-confirm the Shirts-Reinhardt picture, and supplement the recent paper by Kaluza and Robnik.