Abstract
This paper offers a new approach for constructing Kolmogorov - Arnold - Moser (KAM) tori for orbits in the full potential for a non-spherical planet. The Hamilton - Jacobi equation is solved numerically by a Newton-Rhapson iteration, achieving convergence to machine precision, and still retaining literal variable dependence. Similar iteration methods allow correcting the orbital frequencies, and permit the calculation of the state transition matrix for the full problem. Some initial numerical examples are offered.
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