Abstract. 
I will discuss the phenomenon of shear-induced chaos in driven 
dynamical systems. The unforced system is assumed to have 
certain simple structures, such as attracting periodic solutions 
or equilibria undergoing Hopf bifurcations. Specifics of the 
defining equations are unimportant. A geometric mechanism for 
producing chaos is proposed. In the case of periodic kicks 
followed by long relaxations, rigorous results establishing 
the presence of strange attractors with SRB measures are 
presented. These attractors are in a class of chaotic systems 
that can be modeled (roughly) by countable-state Markov chains. 
From this I deduce information on their statistical properties. 
In the last part of this talk, I will return to the phenomenon 
of shear-induced chaos, to explore numerically the range of 
validity of the geometric ideas. Examples including randomly 
forced coupled oscillators will be discussed. I am reporting on
joint works with a number of co-authors.