Transitivity of families in the real line with horizontal asymptotes and vertical asymptotes

Abstract

In the space of increasing transformations without fixed point of the real line with a vertical asymptote, conditions have been shown to determine chaos, but the case with horizontal asymptotes has been little studied. In this work we study this kind of transformations on the real line with a vertical asymptote and two horizontal asymptotes, demonstrating conditions to obtain transitivity and that the set of periodic points is dense on the real line. In addition, it is shown that the existence of periodic orbits of period 2 or 3 eliminate the possibility of transitivity.