Study of the double mathematical pendulum. IV: Ouantitative bounds on values of the system parameters when the homoclinic transversal intersections exist (Q5950742)

[For part I, II, III see the author, Regul. Chaotic Dyn. 4, No. 1, 104--116 (1999; Zbl 0999.70022); J. Phys. A, Math. Gen. 34, No. 49, 11011--11031 (2001; Zbl 1098.70530); Regul. Chaotic Dyn. 5, No. 3, 329--343 (2000; Zbl 0993.34036).] The author considers the so-called reduced double pendulum system which is obtained from the double pendulum in the limit when the ratio of pendulum masses tends to zero. For this system he finds some conditions on the ratio of the lengths of pendula and on the value of the energy under which the system has a hyperbolic periodic trajectory with transversally intersecting invariant manifolds. These conditions correspond to cases when the values of these two parameters are close to zero or infinity.