  In this paper we study homoclinic tangles formed by transversal intersections
of the stable and the unstable manifold of a {\it non-resonant, dissipative}
homoclinic saddle point in periodically perturbed second order equations. We
prove that the dynamics of these homoclinic tangles are that of {\it infinitely
wrapped horseshoe maps}. Using $\mu$ as a parameter representing the magnitude
of the perturbations, we prove that (a) there exist infinitely many disjoint
open intervals of $\mu$, accumulating at $\mu = 0$, such that the entire
homoclinic tangle of the perturbed equation consists of one single horseshoe of
infinitely many symbols, (b) there are parameters in between each of these
parameter intervals, such that the homoclinic tangle contains attracting
periodic solutions, and (c) there are also parameters in between where the
homoclinic tangles admit non-degenerate transversal homoclinic tangency of
certain dissipative hyperbolic periodic solutions. In particular, (c) implies
the existence of strange attractors with SRB measures for a positive measure
set of parameters.
