Revista de la
Unión Matemática Argentina
Families of transitive maps on $\mathbb{R}$ with horizontal asymptotes
Bladismir Leal, Guelvis Mata, Sergio Muñoz
Volume 59, no. 2 (2018), pp. 375–387


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We will prove the existence of a class of transitive maps on the real line $ \mathbb{R} $, with a discontinuity and horizontal asymptotes, whose set of periodic orbits is dense in $ \mathbb{R} $; that is, a class of chaotic families. In addition, we will show a rare phenomenon: the existence of periodic orbits of period three prevents the existence of transitivity.