Study of the Double Mathematical Pendulum — IV. Quantitative Bounds on Values of the System Parameters when the Homoclinic Transversal Intersections Exist

We consider the double mathematical pendulum in the limit of small ratio of pendulum masses. Besides we assume that values of other two system parameters are close to the degenerate ones (i.e. zero or infinity). In these limit cases we prove asymptotic formulae for the homoclinic invariant of some special chosen homoclinic trajectories and obtain quantitative bounds on values of the system parameters when these formulae are valid.