Study of the double mathematical pendulum: II. Investigation of exponentially small homoclinic intersections
نویسنده
چکیده
We consider the double mathematical pendulum in the limit when the ratio of pendulum masses is close to zero and the ratio of pendulum lengths is close to infinity. We found that the limit system has a hyperbolic periodic trajectory, whose invariant manifolds intersect transversally and the intersections are exponentially small. In this case we obtain an asymptotic formula of the homoclinic invariant for the limit system. PACS numbers: 45.20Jj, 02.30.Hq, 05.45.−a
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