Abstract:
This talk contains two parts. In the first we study the 
dynamics of homoclinic tangles in periodically perturbed second order 
equations. 

The second part of this talk is about the chaotic dynamics in non- 
autonomous equations without any periodicity. We prove the existences 
of a spectrum of dynamical scenarios, including new dynamical struc- 
tures that generalize Smale’s horseshoe. In particular, we illustrate 
that transversal intersections of the stable and unstable manifolds of 
the perturbed saddle are neither necessary nor sufficient for chaotic 
dynamics to emerge.