Abstract
AbstractWe construct a smooth function g* : IR ℝ IR with such that the equation has a slowly oscillating periodic solution y, and a slowly oscillating solution z* whose phase curve is homoclinic with respect to the orbit o of y in the space C = C0([1,0],IR). For an associated Poincaré map we obtain a transversal homoclinic loop. The proof of transversality employs a criterion which uses oscillation properties of solutions of variational equations. The main result is that the trajectories (ψn)∞‐∞ of the Poincaré map in a neighbourhood of the homoclinic loop form a hyperbolic set on which the motion is chaotic.
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