ABSTRACT
In this chapter we deal with some classes of operators presenting chaotic dynamical behavior. The topic has been systematically studied during the last three decades. In contrast to the remaining chapters, lineability of families of universal vectors –which is the main concern of this one-has received a unified treatment in at least two major publications, namely, the 2009 book by Bayart and Matheron [61] and the 2011 book by Grosse-Erdmann and Peris [237]; see especially chapters 1 and 8 of [61] and chapters 2, 10 and 11 of [237]. Moreover, it should be said that even the mere enumeration of all known results about universality and close topics goes beyond the scope of this book. Consequently, a selection of the most relevant statements will be given in this chapter and, in turn, we will choose the proofs of a sufficient number of such statements, in order to illustrate the main techniques. Appropriate references will be provided for the remaining proofs, and some of these will be left as exercises. Of course, a reasonable updating of results has been tried.
