Abstract The planar circular Hill’s problem is considered, as well as its limiting integrable variant called the Hénon problem, for which the original Hill’s problem is a singular perturbation. Among solutions to the Hénon problem there are a countable number of generating solutions-arcs that are uniquely determined by the condition of successive passage through the origin of coordinates—singular point of equations of motion of the Hill’s problem. Using the generating solutions-arcs as “letters” of a certain “alphabet”, one can compose, according to some rules, the “words”: generating solutions of families of periodic orbits of the Hill’s problem. The sequence of letters in a word determines the order of orbit transfer from one invariant manifold to another, while the set of all properly specified words determine the system’s symbolic dynamics.


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    Title :

    Symmetric periodic solutions of the Hill’s problem. I


    Contributors:

    Published in:

    Cosmic Research ; 51 , 4 ; 275-288


    Publication date :

    2013-07-01


    Size :

    14 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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