Abstract
The motion of a hard sphere between walls, under the influence of a periodic square wave force, is studied analytically to determine the existence of KAM curves. It is shown that their existence depends on the fact that any segment of them can not be transformed by the dynamics into a "folded" structure. It is shown that a special family of KAM curves are the most stable KAM curves in their respective neighborhoods of the phase space. One of these curves constitutes the boundary, such that there exists no KAM curve with smaller momentum for the same value of the position coordinate. Analytic estimates of this boundary in phase space is obtained, and are shown to closely agree with the numerical results. We discuss the fact that the present criterion for the existence of the KAM curves can be applied to a number of other systems.
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