TY - JOUR

T1 - Study of the double mathematical pendulum - II. Investigation of exponentially small homoclinic intersections

AU - Ivanov, A.V.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - статья

VL - 34

SP - 11011

EP - 11031

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 49

ER -